On modules of bounded multiplicities for the symplectic algebras

被引：28

作者：

Britten, DJ ^{[1
]}

Lemire, FW ^{[1
]}

机构：

[1] Univ Windsor, Dept Math, Windsor, ON N9B 3P4, Canada

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1999年 / 351卷 / 08期

关键词：

D O I：

10.1090/S0002-9947-99-02338-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Simple infinite dimensional highest weight modules having bounded weight multiplicities are classified as submodules of a tensor product. Also, it is shown that a simple torsion free module of finite degree tensored with a finite dimensional module is completely reducible.

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收藏

页码：3413 / 3431

页数：19

相关论文

共 13 条

[1] Modules with bounded weight multiplicities for simple Lie algebras [J].

Benkart, G ;

Britten, D ;

Lemire, F .

MATHEMATISCHE ZEITSCHRIFT, 1997, 225 (02) :333-353

[2] A CLASSIFICATION OF SIMPLE LIE MODULES HAVING A 1-DIMENSIONAL WEIGHT SPACE [J].

BRITTEN, DJ ;

LEMIRE, FW .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 299 (02) :683-697

[3] SIMPLE C-N MODULES WITH MULTIPLICITIES-1 AND APPLICATIONS [J].

BRITTEN, DJ ;

HOOPER, J ;

LEMIRE, FW .

CANADIAN JOURNAL OF PHYSICS, 1994, 72 (7-8) :326-335

[4] SIMPLE A(2)-MODULES WITH A FINITE-DIMENSIONAL WEIGHT SPACE [J].

BRITTEN, DJ ;

LEMIRE, FW ;

FUTORNY, VM .

COMMUNICATIONS IN ALGEBRA, 1995, 23 (02) :467-510

[5] The torsion free Pieri formula [J].

Britten, DJ ;

Lemire, FW .

CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1998, 50 (02) :266-289

[6]

DIXMIER J, 1972, B SC MATH, V96, P339

[7]

Dixmier Jacques, 1974, ALGEBRES ENVELOPPANT

[8] LIE-ALGEBRA MODULES WITH FINITE DIMENSIONAL WEIGHT SPACES .1. [J].

FERNANDO, SL .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 322 (02) :757-781

[9]

Jantzen J.C., 1979, LECT NOTES MATH, V750

[10] TENSOR PRODUCT OF A FINITE AND AN INFINITE DIMENSIONAL REPRESENTATION [J].

KOSTANT, B .

JOURNAL OF FUNCTIONAL ANALYSIS, 1975, 20 (04) :257-285