ON REPRESENTATIONS OF RESTRICTED LIE SUPERALGEBRAS

被引：1

作者：

Yao, Yu-Feng ^{[1
]}

机构：

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

来源：

CZECHOSLOVAK MATHEMATICAL JOURNAL | 2014年 / 64卷 / 03期

基金：

中国国家自然科学基金;

关键词：

restricted Lie superalgebra; chi-reduced representation; indecomposable module; simple module; p-character; MODULAR-REPRESENTATIONS; ALGEBRAS;

D O I：

10.1007/s10587-014-0137-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Simple modules for restricted Lie superalgebras are studied. The indecomposability of baby Kac modules and baby Verma modules is proved in some situation. In particular, for the classical Lie superalgebra of type A(n vertical bar 0), the baby Verma modules Z(chi)(lambda) are proved to be simple for any regular nilpotent p-character chi and typical weight lambda. Moreover, we obtain the dimension formulas for projective covers of simple modules with p-characters of standard Levi form.

引用

页码：845 / 856

页数：12

共 21 条

[1] Modular representations of the supergroup Q(n) -: Part II [J].

Brundan, J .

PACIFIC JOURNAL OF MATHEMATICS, 2006, 224 (01) :65-90

[2] Projective representations of symmetric groups via Sergeev duality [J].

Brundan, J ;

Kleshchev, A .

MATHEMATISCHE ZEITSCHRIFT, 2002, 239 (01) :27-68

[3] Modular representations of the supergroup Q (n), I [J].

Brundan, J ;

Kleshchev, A .

JOURNAL OF ALGEBRA, 2003, 260 (01) :64-98

[4] A new proof of the Mullineux conjecture [J].

Brundan, J ;

Kujawa, J .

JOURNAL OF ALGEBRAIC COMBINATORICS, 2003, 18 (01) :13-39

[5] MODULAR REPRESENTATION-THEORY OF LIE-ALGEBRAS [J].

FRIEDLANDER, EM ;

PARSHALL, BJ .

AMERICAN JOURNAL OF MATHEMATICS, 1988, 110 (06) :1055-1093

[6]

Jacobson N., 1962, LIE ALGEBRAS

[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]

Kujawa J, 2006, CONTEMP MATH, V413, P123

[10] IDENTITIES IN THE ENVELOPING-ALGEBRAS FOR MODULAR LIE-SUPERALGEBRAS [J].

PETROGRADSKI, VM .

JOURNAL OF ALGEBRA, 1992, 145 (01) :1-21

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