Super tableaux and a branching rule for the general linear Lie superalgebra

被引：7

作者：

Clark, Sean ^{[1
]}

Peng, Yung-Ning ^{[2
]}

Thamrongpairoj, S. Kuang ^{[1
,3
]}

机构：

[1] Univ Virginia, Dept Math, Charlottesville, VA 22903 USA

[2] Acad Sinica, Inst Math, Taipei, Taiwan

[3] Univ Calif San Diego, Dept Math, San Diego, CA 92103 USA

来源：

LINEAR & MULTILINEAR ALGEBRA | 2015年 / 63卷 / 02期

关键词：

05E10; 17B10; Gelfand-Tsetlin bases; representations; Lie superalgebras; duality; Young diagrams;

D O I：

10.1080/03081087.2013.860599

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note, we formulate and prove a branching rule for simple polynomial modules of the Lie superalgebra . Our branching rules depend on the conjugacy class of a Borel subalgebra. A Gelfand-Tsetlin basis of a polynomial module associated to each Borel subalgebra is obtained in terms of generalized semistandard tableaux.

引用

页码：274 / 282

页数：9

共 12 条

[1] HOOK YOUNG-DIAGRAMS WITH APPLICATIONS TO COMBINATORICS AND TO REPRESENTATIONS OF LIE-SUPERALGEBRAS [J].

BERELE, A ;

REGEV, A .

ADVANCES IN MATHEMATICS, 1987, 64 (02) :118-175

[2]

Cheng S.-J., 2013, GRADUATE STUDIES MAT, V144

[3] Howe Duality and Kostant Homology Formula for Infinite-Dimensional Lie Superalgebras [J].

Cheng, Shun-Jen ;

Kwon, Jae-Hoon .

INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2008, 2008

[4] Super duality and irreducible characters of ortho-symplectic Lie superalgebras [J].

Cheng, Shun-Jen ;

Lam, Ngau ;

Wang, Weiqiang .

INVENTIONES MATHEMATICAE, 2011, 183 (01) :189-224

[5] Howe duality for Lie superalgebras [J].

Cheng, SJ ;

Wang, WQ .

COMPOSITIO MATHEMATICA, 2001, 128 (01) :55-94

[6]

Goodman R., 2009, GTM, V255

[7] LIE SUPER-ALGEBRAS [J].

KAC, VG .

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

[8] Rational sernistandard tableaux and character formula for the Lie superalgebra (gI)over-cap∞|∞ [J].

Kwon, Jae-Hoon .

ADVANCES IN MATHEMATICS, 2008, 217 (02) :713-739

[9]

Molev AI, 2006, HBK ALGEBR, V4, P109, DOI 10.1016/S1570-7954(06)80006-9

[10]

Sagan B., 2001, GTM, V203

← 1 2 →