22:
816:
2519:
1195:
565:
811:{\displaystyle {\begin{array}{ccc}GL(\mathbf {d} )\times \operatorname {Rep} (Q,\mathbf {d} )&\longrightarrow &\operatorname {Rep} (Q,\mathbf {d} )\\{\Big (}(g_{i}),(V_{i},V(\alpha )){\Big )}&\longmapsto &(V_{i},g_{t(\alpha )}\cdot V(\alpha )\cdot g_{s(\alpha )}^{-1})\end{array}}}
1036:
1818:
2157:
532:
395:
1612:
2878:
1457:
850:
1623:
1957:
1172:
415:
2222:
1890:
1296:
300:
1512:
2319:
288:
187:
2610:
51:
1324:
228:)) by simultaneous base change. Such action induces one on the ring of functions. The ones which are invariants up to a character of the group are called
1031:{\displaystyle {\begin{array}{ccc}GL(\mathbf {d} )\times k&\longrightarrow &k\\(g,f)&\longmapsto &g\cdot f(-):=f(g^{-1}.-)\end{array}}}
1813:{\displaystyle SI(Q,\mathbf {d} )_{\sigma }:=\{f\in k:g\cdot f=\prod _{i\in Q_{0}}\det(g_{i})^{\sigma _{i}}f,\forall g\in GL(\mathbf {d} )\}.}
73:
2152:{\displaystyle (g_{1},g_{2})\cdot {\det }^{u}(B)={\det }^{u}(g_{2}^{-1}Bg_{1})={\det }^{u}(g_{1}){\det }^{-u}(g_{2}){\det }^{u}(B)}
527:{\displaystyle \bigoplus _{\alpha \in Q_{1}}\operatorname {Hom} _{k}(k^{\mathbf {d} (s(\alpha ))},k^{\mathbf {d} (t(\alpha ))})}
3025:
1084:
99:
2241:
2168:
1851:
3020:
34:
3015:
44:
38:
30:
2903:
390:{\displaystyle \operatorname {Rep} (Q,\mathbf {d} ):=\{V\in \operatorname {Rep} (Q):V_{i}=\mathbf {d} (i)\}}
1607:{\displaystyle SI(Q,\mathbf {d} )=\bigoplus _{\sigma \in \mathbb {Z} ^{Q_{0}}}SI(Q,\mathbf {d} )_{\sigma }}
2518:
55:
1223:
261:
233:
87:
2302:
271:
170:
2995:
1194:
2938:"A classification of irreducible prehomogeneous vector spaces and their relative invariants."
2979:
2949:
2915:
2873:{\displaystyle SI(Q,\mathbf {d} )={\frac {k}{D_{1,2}D_{3,4}+D_{1,4}D_{2,3}-D_{1,3}D_{2,4}}}}
2991:
2963:
2929:
2452:
Skowronski–Weyman provided a geometric characterization of the class of tame quivers (i.e.
2987:
2959:
2925:
2344:
Furthermore, we have an interpretation for the generators of this polynomial algebra. Let
210:
855:
570:
232:. They form a ring whose structure reflects representation-theoretical properties of the
2510:
2476:
2472:
2457:
2453:
2253:
2233:
1475:-dimensional semi-simple representation, therefore any invariant function is constant.
3009:
2999:
2390:
s are arranged in increasing order with respect to the codimension so that the first
1452:{\displaystyle \det(A-t\mathbb {I} )=t^{n}-c_{1}(A)t^{n-1}+\cdots +(-1)^{n}c_{n}(A)}
2904:"Semi-invariants of quivers and saturation for Littlewood–Richardson coefficients."
2889:
2970:
Skowronski, A.; Weyman, J. (2000), "The algebras of semi-invariants of quivers.",
2920:
2937:
163:) are, respectively, the starting and the ending vertices of α. Given an element
2954:
2162:
The ring of semi-invariants equals the polynomial ring generated by det, i.e.
1506:), with a richer structure called ring of semi-invariants. It decomposes as
2260:
a dimension vector. Let Σ be the set of weights σ such that there exists
537:
Such affine variety is endowed with an action of the algebraic group GL(
2983:
2437:) consisting of invertible matrices. Then we immediately recover SI(Q,(
2244:. Sato and Kimura described the ring of semi-invariants in such case.
2228:
Characterization of representation type through semi-invariant theory
1863:
2277:
non-zero and irreducible. Then the following properties hold true.
2468:
Let Q be a finite connected quiver. The following are equivalent:
1478:
Elements which are invariants with respect to the subgroup SL(
15:
2232:
For quivers of finite representation-type, that is to say
2604:). Such functions generate the ring of semi-invariants:
1318:), as the coefficients of the characteristic polynomial
1217:) is given by usual conjugation. The invariant ring is
1167:{\displaystyle I(Q,\mathbf {d} ):=k^{GL(\mathbf {d} )}}
1471:
has a unique closed orbit corresponding to the unique
2613:
2305:
2171:
1960:
1854:
1626:
1515:
1327:
1226:
1087:
853:
568:
418:
303:
274:
173:
2501:) is either a polynomial algebra or a hypersurface.
2240:
admits an open dense orbit. In other words, it is a
2299:ii) All weights in Σ are linearly independent over
1911:is congruent to the set of square matrices of size
1467:In case Q has neither loops nor cycles the variety
2872:
2381:is closed and irreducible. We can assume that the
2313:
2216:
2151:
1884:
1812:
1606:
1451:
1290:
1166:
1030:
810:
526:
389:
282:
181:
840:We have an induced action on the coordinate ring
709:
652:
2217:{\displaystyle {\mathsf {SI}}(Q,\mathbf {d} )=k}
2208:
2130:
2099:
2071:
2019:
1995:
1885:{\displaystyle 1{\xrightarrow {\ \ \alpha \ }}2}
1739:
1328:
189:, the set of representations of Q with dim
43:but its sources remain unclear because it lacks
559:)) by simultaneous base change on each vertex:
2398:is the zero-set of the irreducible polynomial
209:It is naturally endowed with an action of the
409:this can be identified with the vector space
8:
1804:
1660:
384:
330:
1054:is called an invariant (with respect to GL(
2328:) is the polynomial ring generated by the
2953:
2919:
2855:
2839:
2820:
2804:
2785:
2769:
2748:
2729:
2710:
2691:
2672:
2653:
2640:
2629:
2612:
2307:
2306:
2304:
2191:
2173:
2172:
2170:
2134:
2129:
2119:
2103:
2098:
2088:
2075:
2070:
2057:
2041:
2036:
2023:
2018:
1999:
1994:
1981:
1968:
1959:
1858:
1853:
1796:
1764:
1759:
1749:
1731:
1720:
1690:
1651:
1642:
1625:
1598:
1589:
1564:
1559:
1555:
1554:
1546:
1531:
1514:
1434:
1424:
1390:
1371:
1358:
1344:
1343:
1326:
1279:
1260:
1239:
1225:
1154:
1144:
1132:
1100:
1086:
1006:
938:
899:
867:
854:
852:
833:) are isomorphic if and only if their GL(
792:
778:
741:
728:
708:
707:
683:
664:
651:
650:
638:
608:
582:
569:
567:
496:
495:
463:
462:
446:
434:
423:
417:
370:
361:
319:
302:
294:-dimensional representations is given by
276:
275:
273:
175:
174:
172:
74:Learn how and when to remove this message
1833:is called semi-invariant of weight
400:Once fixed bases for each vector space
2421:In the example above the action of GL(
2177:
2174:
7:
1291:{\displaystyle I(Q,\mathbf {d} )=k}
1943:)) is a semi-invariant of weight (
1778:
1209:) the representation space is End(
14:
2280:i) For every weight σ we have dim
1923:). The function defined, for any
2902:Derksen, H.; Weyman, J. (2000),
2630:
2537:can be identified with a 4-ple (
2517:
2192:
1797:
1691:
1643:
1590:
1532:
1240:
1193:
1155:
1133:
1101:
939:
900:
868:
639:
609:
583:
497:
464:
371:
320:
111:to each vertex and a linear map
20:
2493:iii) For each dimension vector
2460:) in terms of semi-invariants.
2760:
2646:
2634:
2620:
2482:ii) For each dimension vector
2211:
2205:
2196:
2182:
2146:
2140:
2125:
2112:
2094:
2081:
2063:
2029:
2011:
2005:
1987:
1961:
1801:
1793:
1756:
1742:
1698:
1695:
1681:
1672:
1648:
1633:
1595:
1580:
1536:
1522:
1446:
1440:
1421:
1411:
1383:
1377:
1348:
1331:
1285:
1253:
1244:
1230:
1189:Consider the 1-loop quiver Q:
1177:is in general a subalgebra of
1159:
1151:
1141:
1137:
1123:
1114:
1105:
1091:
1021:
999:
990:
984:
970:
965:
953:
946:
943:
929:
920:
912:
907:
904:
890:
881:
872:
864:
801:
788:
782:
768:
762:
751:
745:
721:
716:
704:
701:
695:
676:
670:
657:
643:
629:
618:
613:
599:
587:
579:
521:
516:
513:
507:
501:
483:
480:
474:
468:
455:
381:
375:
351:
345:
324:
310:
264:. Consider a dimension vector
206:has a vector space structure.
1:
2936:Sato, M.; Kimura, T. (1977),
2921:10.1090/S0894-0347-00-00331-3
2582:the function defined on each
1823:A function belonging to SI(Q,
2490:) is complete intersection.
2314:{\displaystyle \mathbb {Q} }
283:{\displaystyle \mathbb {N} }
182:{\displaystyle \mathbb {N} }
102:of Q assigns a vector space
3042:
2529:= (1,1,1,1,2). An element
2525:Pick the dimension vector
2394:have codimension one and Z
2242:prehomogenous vector space
821:By definition two modules
2955:10.1017/S0027763000017633
2464:Skowronski–Weyman theorem
1078:). The set of invariants
2348:be the open orbit, then
268:, that is an element in
90:Q with set of vertices Q
86:In mathematics, given a
29:This article includes a
2429:) has an open orbit on
1845:Consider the quiver Q:
1310:s are defined, for any
1213:) and the action of GL(
58:more precise citations.
2874:
2315:
2218:
2153:
1886:
1814:
1608:
1453:
1292:
1168:
1032:
812:
528:
391:
284:
183:
3026:Representation theory
2875:
2316:
2219:
2154:
1887:
1815:
1609:
1502:)) form a ring, SI(Q,
1454:
1293:
1169:
1042:Polynomial invariants
1033:
813:
529:
392:
285:
184:
2611:
2303:
2169:
1958:
1852:
1624:
1513:
1325:
1224:
1085:
851:
566:
416:
301:
272:
171:
2908:J. Amer. Math. Soc.
2497:, the algebra SI(Q,
2486:, the algebra SI(Q,
2248:Sato–Kimura theorem
2236:, the vector space
2049:
1876:
837:)-orbits coincide.
800:
94:and set of arrows Q
2984:10.1007/bf01234798
2870:
2311:
2214:
2149:
2032:
1882:
1810:
1738:
1604:
1573:
1449:
1288:
1164:
1028:
1026:
808:
806:
774:
524:
441:
387:
280:
179:
31:list of references
2972:Transform. Groups
2868:
2565:) of matrices in
2471:i) Q is either a
2458:Euclidean quivers
1877:
1875:
1869:
1866:
1716:
1542:
419:
143:)) to each arrow
84:
83:
76:
3033:
3021:Invariant theory
3002:
2966:
2957:
2932:
2923:
2879:
2877:
2876:
2871:
2869:
2867:
2866:
2865:
2850:
2849:
2831:
2830:
2815:
2814:
2796:
2795:
2780:
2779:
2763:
2759:
2758:
2740:
2739:
2721:
2720:
2702:
2701:
2683:
2682:
2664:
2663:
2641:
2633:
2521:
2511:Euclidean quiver
2477:Euclidean quiver
2320:
2318:
2317:
2312:
2310:
2223:
2221:
2220:
2215:
2195:
2181:
2180:
2158:
2156:
2155:
2150:
2139:
2138:
2133:
2124:
2123:
2111:
2110:
2102:
2093:
2092:
2080:
2079:
2074:
2062:
2061:
2048:
2040:
2028:
2027:
2022:
2004:
2003:
1998:
1986:
1985:
1973:
1972:
1907:). In this case
1891:
1889:
1888:
1883:
1878:
1873:
1867:
1864:
1859:
1819:
1817:
1816:
1811:
1800:
1771:
1770:
1769:
1768:
1754:
1753:
1737:
1736:
1735:
1694:
1656:
1655:
1646:
1613:
1611:
1610:
1605:
1603:
1602:
1593:
1572:
1571:
1570:
1569:
1568:
1558:
1535:
1458:
1456:
1455:
1450:
1439:
1438:
1429:
1428:
1401:
1400:
1376:
1375:
1363:
1362:
1347:
1297:
1295:
1294:
1289:
1284:
1283:
1265:
1264:
1243:
1197:
1173:
1171:
1170:
1165:
1163:
1162:
1158:
1136:
1104:
1037:
1035:
1034:
1029:
1027:
1014:
1013:
942:
903:
871:
817:
815:
814:
809:
807:
799:
791:
755:
754:
733:
732:
713:
712:
688:
687:
669:
668:
656:
655:
642:
612:
586:
533:
531:
530:
525:
520:
519:
500:
487:
486:
467:
451:
450:
440:
439:
438:
396:
394:
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388:
374:
366:
365:
323:
289:
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286:
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178:
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72:
68:
65:
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54:this article by
45:inline citations
24:
23:
16:
3041:
3040:
3036:
3035:
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3032:
3031:
3030:
3016:Directed graphs
3006:
3005:
2969:
2942:Nagoya Math. J.
2935:
2914:(13): 467–479,
2901:
2898:
2886:
2851:
2835:
2816:
2800:
2781:
2765:
2764:
2744:
2725:
2706:
2687:
2668:
2649:
2642:
2609:
2608:
2603:
2594:
2581:
2564:
2557:
2550:
2543:
2507:
2466:
2419:
2404:
2397:
2389:
2380:
2371:
2362:
2336:
2301:
2300:
2295:
2285:
2276:
2268:
2250:
2230:
2167:
2166:
2128:
2115:
2097:
2084:
2069:
2053:
2017:
1993:
1977:
1964:
1956:
1955:
1850:
1849:
1843:
1832:
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1647:
1622:
1621:
1594:
1560:
1553:
1511:
1510:
1493:
1491:
1465:
1463:Semi-invariants
1430:
1420:
1386:
1367:
1354:
1323:
1322:
1309:
1275:
1256:
1222:
1221:
1187:
1140:
1083:
1082:
1044:
1025:
1024:
1002:
973:
968:
950:
949:
915:
910:
849:
848:
805:
804:
737:
724:
719:
714:
679:
660:
647:
646:
621:
616:
564:
563:
550:
549:
491:
458:
442:
430:
414:
413:
408:
357:
299:
298:
270:
269:
251:
247:
242:
230:semi-invariants
219:
218:
211:algebraic group
197:
169:
168:
110:
97:
93:
80:
69:
63:
60:
49:
35:related reading
25:
21:
12:
11:
5:
3039:
3037:
3029:
3028:
3023:
3018:
3008:
3007:
3004:
3003:
2978:(4): 361–402,
2967:
2933:
2897:
2894:
2893:
2892:
2885:
2882:
2881:
2880:
2864:
2861:
2858:
2854:
2848:
2845:
2842:
2838:
2834:
2829:
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2823:
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2813:
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2803:
2799:
2794:
2791:
2788:
2784:
2778:
2775:
2772:
2768:
2762:
2757:
2754:
2751:
2747:
2743:
2738:
2735:
2732:
2728:
2724:
2719:
2716:
2713:
2709:
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2700:
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2690:
2686:
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2678:
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2667:
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2659:
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2652:
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2639:
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2599:
2590:
2573:
2562:
2555:
2548:
2541:
2523:
2522:
2506:
2503:
2465:
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2418:
2415:
2402:
2395:
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2376:
2367:
2360:
2332:
2309:
2291:
2281:
2274:
2264:
2249:
2246:
2234:Dynkin quivers
2229:
2226:
2225:
2224:
2213:
2210:
2207:
2204:
2201:
2198:
2194:
2190:
2187:
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39:external links
28:
26:
19:
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10:
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4:
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2:
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2509:Consider the
2504:
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2500:
2496:
2491:
2489:
2485:
2480:
2478:
2474:
2473:Dynkin quiver
2469:
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2254:Dynkin quiver
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861:
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847:
846:
845:
844:by defining:
843:
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832:
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296:
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293:
290:. The set of
267:
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235:
231:
227:
223:
212:
207:
205:
202:(i) for each
201:
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138:
134:
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126:
122:
118:
114:
109:
105:
101:
89:
78:
75:
67:
57:
53:
47:
46:
40:
36:
32:
27:
18:
17:
2975:
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2941:
2911:
2907:
2890:Wild problem
2600:
2596:
2591:
2587:
2583:
2578:
2574:
2570:
2569:(1,2). Call
2566:
2559:
2552:
2545:
2538:
2534:
2530:
2526:
2524:
2508:
2498:
2494:
2492:
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2451:
2446:
2442:
2438:
2434:
2430:
2426:
2422:
2420:
2410:
2406:
2405:, then SI(Q,
2399:
2391:
2386:
2382:
2377:
2373:
2368:
2364:
2357:
2353:
2349:
2345:
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2257:
2251:
2237:
2231:
2161:
1948:
1944:
1940:
1936:
1932:
1928:
1924:
1920:
1916:
1912:
1908:
1904:
1900:
1896:
1894:
1844:
1834:
1829:
1824:
1822:
1616:
1503:
1499:
1495:
1485:
1479:
1477:
1472:
1468:
1466:
1315:
1311:
1306:
1302:
1300:
1214:
1210:
1206:
1202:
1200:
1188:
1178:
1176:
1075:
1071:
1067:
1063:
1059:
1055:
1051:
1047:
1045:
841:
839:
834:
830:
826:
822:
820:
556:
552:
543:
538:
536:
405:
401:
399:
291:
265:
257:
253:
243:
229:
225:
221:
208:
203:
199:
194:
190:
164:
160:
156:
152:
148:
144:
140:
136:
132:
128:
124:
120:
116:
112:
107:
103:
85:
70:
61:
50:Please help
42:
2372:where each
2252:Let Q be a
1482:) := Π
1046:An element
541:) := Π
240:Definitions
56:introducing
3010:Categories
2896:References
2324:iii) SI(Q,
1951:) in fact
1935:), as det(
1301:where the
244:Let Q = (Q
3000:120708005
2948:: 1–155,
2833:−
2105:−
2043:−
1991:⋅
1871:α
1785:∈
1779:∀
1762:σ
1725:∈
1718:∏
1708:⋅
1679:
1667:∈
1653:σ
1600:σ
1551:∈
1548:σ
1544:⨁
1415:−
1406:⋯
1395:−
1365:−
1338:−
1270:…
1121:
1019:−
1008:−
988:−
979:⋅
971:⟼
927:
913:⟶
888:
876:×
794:−
786:α
772:⋅
766:α
757:⋅
749:α
717:⟼
699:α
627:
619:⟶
597:
591:×
511:α
478:α
453:
428:∈
425:α
421:⨁
343:
337:∈
308:
64:June 2020
2884:See also
2363:∪ ... ∪
1861:→
1070:for any
829:∈ Rep(Q,
147:, where
2992:1800533
2964:0430336
2930:1758750
2586:as det(
2505:Example
2417:Example
2269:∈ SI(Q,
1841:Example
1185:Example
260:) be a
52:improve
2998:
2990:
2962:
2928:
2454:Dynkin
1874:
1868:
1865:
1617:where
1314:∈ End(
1058:)) if
262:quiver
234:quiver
88:quiver
2996:S2CID
2475:or a
2445:)) =
2341:∈ Σ.
2296:≤ 1.
2286:SI(Q,
1074:∈ GL(
131:)) →
37:, or
2456:and
2409:) =
2337:'s,
1895:Fix
1201:For
98:, a
2980:doi
2950:doi
2916:doi
2513:Q:
2209:det
2131:det
2100:det
2072:det
2020:det
1996:det
1899:= (
1740:det
1676:Rep
1494:SL(
1488:∈ Q
1329:det
1205:= (
1118:Rep
924:Rep
885:Rep
624:Rep
594:Rep
551:GL(
546:∈ Q
444:Hom
340:Rep
305:Rep
220:GL(
215:i∈Q
155:),
119:):
3012::
2994:,
2988:MR
2986:,
2974:,
2960:MR
2958:,
2946:65
2944:,
2940:,
2926:MR
2924:,
2910:,
2906:,
2558:,
2551:,
2544:,
2533:∈
2479:.
2449:.
2413:.
2356:=
2352:\
2321:.
2256:,
1947:,−
1927:∈
1915::
1837:.
1658::=
1181:.
1109::=
1066:=
1050:∈
994::=
328::=
248:,Q
236:.
198:=
167:∈
41:,
33:,
2982::
2976:5
2952::
2918::
2912:3
2863:4
2860:,
2857:2
2853:D
2847:3
2844:,
2841:1
2837:D
2828:3
2825:,
2822:2
2818:D
2812:4
2809:,
2806:1
2802:D
2798:+
2793:4
2790:,
2787:3
2783:D
2777:2
2774:,
2771:1
2767:D
2761:]
2756:4
2753:,
2750:2
2746:D
2742:,
2737:3
2734:,
2731:1
2727:D
2723:,
2718:3
2715:,
2712:2
2708:D
2704:,
2699:4
2696:,
2693:1
2689:D
2685:,
2680:4
2677:,
2674:3
2670:D
2666:,
2661:2
2658:,
2655:1
2651:D
2647:[
2644:k
2638:=
2635:)
2631:d
2627:,
2624:Q
2621:(
2618:I
2615:S
2601:j
2597:A
2595:,
2592:i
2588:A
2584:V
2579:j
2577:,
2575:i
2571:D
2567:M
2563:4
2560:A
2556:3
2553:A
2549:2
2546:A
2542:1
2539:A
2535:k
2531:V
2527:d
2499:d
2495:d
2488:d
2484:d
2447:k
2443:n
2441:,
2439:n
2435:n
2433:(
2431:M
2427:n
2425:,
2423:n
2411:k
2407:d
2403:1
2400:f
2396:i
2392:l
2387:i
2383:Z
2378:i
2374:Z
2369:t
2365:Z
2361:1
2358:Z
2354:O
2350:k
2346:O
2339:σ
2334:σ
2330:f
2326:d
2308:Q
2293:σ
2290:)
2288:d
2283:k
2275:σ
2273:)
2271:d
2266:σ
2262:f
2258:d
2238:k
2212:]
2206:[
2203:k
2200:=
2197:)
2193:d
2189:,
2186:Q
2183:(
2178:I
2175:S
2147:)
2144:B
2141:(
2136:u
2126:)
2121:2
2117:g
2113:(
2108:u
2095:)
2090:1
2086:g
2082:(
2077:u
2067:=
2064:)
2059:1
2055:g
2051:B
2046:1
2038:2
2034:g
2030:(
2025:u
2015:=
2012:)
2009:B
2006:(
2001:u
1988:)
1983:2
1979:g
1975:,
1970:1
1966:g
1962:(
1949:u
1945:u
1941:α
1939:(
1937:B
1933:n
1931:(
1929:M
1925:B
1921:n
1919:(
1917:M
1913:n
1909:k
1905:n
1903:,
1901:n
1897:d
1880:2
1856:1
1835:σ
1830:σ
1827:)
1825:d
1808:.
1805:}
1802:)
1798:d
1794:(
1791:L
1788:G
1782:g
1776:,
1773:f
1766:i
1757:)
1751:i
1747:g
1743:(
1733:0
1729:Q
1722:i
1714:=
1711:f
1705:g
1702::
1699:]
1696:)
1692:d
1688:,
1685:Q
1682:(
1673:[
1670:k
1664:f
1661:{
1649:)
1644:d
1640:,
1637:Q
1634:(
1631:I
1628:S
1596:)
1591:d
1587:,
1584:Q
1581:(
1578:I
1575:S
1566:0
1562:Q
1556:Z
1540:=
1537:)
1533:d
1529:,
1526:Q
1523:(
1520:I
1517:S
1504:d
1500:i
1498:(
1496:d
1492:}
1490:0
1486:i
1484:{
1480:d
1473:d
1469:k
1447:)
1444:A
1441:(
1436:n
1432:c
1426:n
1422:)
1418:1
1412:(
1409:+
1403:+
1398:1
1392:n
1388:t
1384:)
1381:A
1378:(
1373:1
1369:c
1360:n
1356:t
1352:=
1349:)
1345:I
1341:t
1335:A
1332:(
1316:k
1312:A
1307:i
1303:c
1286:]
1281:n
1277:c
1273:,
1267:,
1262:1
1258:c
1254:[
1251:k
1248:=
1245:)
1241:d
1237:,
1234:Q
1231:(
1228:I
1215:n
1211:k
1207:n
1203:d
1179:k
1160:)
1156:d
1152:(
1149:L
1146:G
1142:]
1138:)
1134:d
1130:,
1127:Q
1124:(
1115:[
1112:k
1106:)
1102:d
1098:,
1095:Q
1092:(
1089:I
1076:d
1072:g
1068:f
1064:f
1062:⋅
1060:g
1056:d
1052:k
1048:f
1022:)
1016:.
1011:1
1004:g
1000:(
997:f
991:)
985:(
982:f
976:g
966:)
963:f
960:,
957:g
954:(
947:]
944:)
940:d
936:,
933:Q
930:(
921:[
918:k
908:]
905:)
901:d
897:,
894:Q
891:(
882:[
879:k
873:)
869:d
865:(
862:L
859:G
842:k
835:d
831:d
827:N
825:,
823:M
802:)
797:1
789:)
783:(
780:s
776:g
769:)
763:(
760:V
752:)
746:(
743:t
739:g
735:,
730:i
726:V
722:(
710:)
705:)
702:)
696:(
693:V
690:,
685:i
681:V
677:(
674:,
671:)
666:i
662:g
658:(
653:(
644:)
640:d
636:,
633:Q
630:(
614:)
610:d
606:,
603:Q
600:(
588:)
584:d
580:(
577:L
574:G
557:i
555:(
553:d
548:0
544:i
539:d
522:)
517:)
514:)
508:(
505:t
502:(
498:d
493:k
489:,
484:)
481:)
475:(
472:s
469:(
465:d
460:k
456:(
448:k
436:1
432:Q
406:i
402:V
385:}
382:)
379:i
376:(
372:d
368:=
363:i
359:V
355::
352:)
349:Q
346:(
334:V
331:{
325:)
321:d
317:,
314:Q
311:(
292:d
277:N
266:d
258:t
256:,
254:s
252:,
250:1
246:0
226:i
224:(
222:d
217:0
213:Π
204:i
200:d
195:i
191:V
176:N
165:d
161:α
159:(
157:t
153:α
151:(
149:s
145:α
141:α
139:(
137:t
135:(
133:V
129:α
127:(
125:s
123:(
121:V
117:α
115:(
113:V
108:i
104:V
96:1
92:0
77:)
71:(
66:)
62:(
48:.
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