Some Weyl modules and cohomology for algebraic groups

被引：3

作者：

Ibraev, Sh. Sh. ^{[1
,2
]}

机构：

[1] Korkyt Ata Kyzylorda State Univ, Kyzylorda 120014, Kazakhstan

[2] Inst Math & Math Modeling, Alma Ata, Kazakhstan

来源：

COMMUNICATIONS IN ALGEBRA | 2020年 / 48卷 / 09期

关键词：

Algebraic group; cohomology; Jantzen filtration; Weyl module; IRREDUCIBLE CHARACTERS; REPRESENTATIONS;

D O I：

10.1080/00927872.2020.1749647

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we give a generalization of O'Halloran's theorem that gives rise to families of Weyl modules with simple radicals. This generalization is then applied to simply connected, semisimple algebraic groups of types B, C, and D. We also construct families of Weyl modules with formal characters of length 4, and compute the extensions and cohomology of simple modules associated with these Weyl modules.

引用

页码：3859 / 3873

页数：15

共 16 条

[1] Some simple modules for classical groups and p-ranks of orthogonal and Hermitian geometries [J].

Arslan, Ogul ;

Sin, Peter .

JOURNAL OF ALGEBRA, 2011, 327 (01) :141-169

[2] RESTRICTED REPRESENTATIONS OF CLASSICAL LIE ALGEBRAS OF TYPES A2 AND B2 [J].

BRADEN, B .

BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1967, 73 (03) :482-&

[3] On certain submodules ofWeyl modules for SO(2n+1, F) with char(F)=2 [J].

Cardinali, Ilaria ;

Pasini, Antonio .

JOURNAL OF GROUP THEORY, 2014, 17 (04) :559-588

[4]

Cavallin M, 2017, STRUCTURE CERTAIN WE

[5] ABSTRACT KAZHDAN-LUSZTIG THEORIES [J].

CLINE, E ;

PARSHALL, B ;

SCOTT, L .

TOHOKU MATHEMATICAL JOURNAL, 1993, 45 (04) :511-534

[6]

Dowd MF, 1996, COMMUN ALGEBRA, V24, P2597

[7] Submodule structure of some Weyl modules and the cohomology for SO2l(K) [J].

Ibraev, Sh Sh .

COMMUNICATIONS IN ALGEBRA, 2019, 47 (09) :3735-3764

[8]

Jantzen J. C., 2003, REPRESENTATIONS ALGE, V107, DOI [10.1090/surv/107, DOI 10.1090/SURV/107]

[9]

Jantzen J.C., 1980, Finite Simple Groups II, P291

[10] ESTIMATIONS OF G(N) [J].

JANTZEN, JC .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1977, 290 :117-141

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