On Blocks in Restricted Representations of Lie Superalgebras of Cartan Type

被引：1

作者：

Duan, Fei Fei ^{[1
]}

Shu, Bin ^{[2
]}

Yao, Yu Feng ^{[3
]}

机构：

[1] Hebei Normal Univ, Sch Math Sci, Shijiazhuang 050024, Hebei, Peoples R China

[2] East China Normal Univ, Sch Math Sci, Shanghai 200241, Peoples R China

[3] Shanghai Maritime Univ, Dept Math, Shanghai 201306, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2020年 / 36卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Lie superalgebra of Cartan type; restricted representation; block; ALGEBRAS;

D O I：

10.1007/s10114-020-9469-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let g be a restricted Lie superalgebra of Cartan typeW(n),S(n)orH(n) over an algebraically closed fieldkof prime characteristicp> 3, in the sense of modular version of Kac's definition in 1977. In this note, we show that the restricted representation category overghas only one block (reckoning parities in). This phenomenon is very different from the case of characteristic zero.

引用

页码：1061 / 1075

页数：15

共 16 条

[1] THE BRUNDAN-KAZHDAN-LUSZTIG CONJECTURE FOR GENERAL LINEAR LIE SUPERALGEBRAS [J].

Cheng, Shun-Jen ;

Lam, Ngau ;

Wang, Weiqiang .

DUKE MATHEMATICAL JOURNAL, 2015, 164 (04) :617-695

[2]

Duan F. F., ARXIV190806251MATHRT

[3] Representations of the Witt Lie Superalgebra with p-character of Height One [J].

Duan, Feifei .

ALGEBRAS AND REPRESENTATION THEORY, 2016, 19 (04) :873-893

[4] Cartan invariants for the Witt superalgebra W(2) in positive characteristic [J].

Duan, Feifei ;

Li, Fang .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2016, 15 (03)

[5]

GORDON R, 1982, J ALGEBRA, V76, P111, DOI 10.1016/0021-8693(82)90240-X

[6] BLOCK DEGENERACY AND CARTAN INVARIANTS FOR GRADED LIE-ALGEBRAS OF CARTAN TYPE [J].

HOLMES, RR ;

NAKANO, DK .

JOURNAL OF ALGEBRA, 1993, 161 (01) :155-170

[7]

Jantzen JC, 1998, NATO ADV SCI I C-MAT, V514, P185

[8] LIE SUPER-ALGEBRAS [J].

KAC, VG .

ADVANCES IN MATHEMATICS, 1977, 26 (01) :8-96

[9] Blocks of Lie superalgebras of type W(n) [J].

Shomron, N .

JOURNAL OF ALGEBRA, 2002, 251 (02) :739-750

[10] The generalized restricted representations of graded Lie algebras of Cartan type [J].

Shu, B .

JOURNAL OF ALGEBRA, 1997, 194 (01) :157-177

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