Combinatorial Howe duality of symplectic type

被引：1

作者：

Heo, Taehyeok ^{[1
]}

Kwon, Jae-Hoon ^{[1
,2
]}

机构：

[1] Seoul Natl Univ, Dept Math Sci, Seoul 08826, South Korea

[2] Seoul Natl Univ, RIM, Seoul 08826, South Korea

来源：

JOURNAL OF ALGEBRA | 2022年 / 600卷

基金：

新加坡国家研究基金会;

关键词：

Quantum group; Crystal graphs; Howe duality; RSK correspondence; Jeu de taquin; SCHENSTED-TYPE CORRESPONDENCE; TYPES B; LIE; TABLEAUX; REPRESENTATIONS; SUPERALGEBRAS; TAQUIN; JEU;

D O I：

10.1016/j.jalgebra.2022.01.037

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a new combinatorial interpretation of Howe dual pairs of the form (g ,Sp(2l)), where g is a Lie (super)algebra of classical type. This is done by establishing a symplectic analogue of the RSK algorithm associated to this pair, in a uniform way which does not depend on g. We introduce an analogue of jeu de taquin sliding for spinor model of irreducible characters of a Lie superalgebra g to define a P-tableau and show that the associated Q-tableau is given by a symplectic tableau due to King. (c) 2022 Elsevier Inc. All rights reserved.

引用

页码：1 / 44

页数：44

共 39 条

[1] [Anonymous], 1985, Lect. in App. Math.
[2] HOOK YOUNG-DIAGRAMS WITH APPLICATIONS TO COMBINATORICS AND TO REPRESENTATIONS OF LIE-SUPERALGEBRAS
BERELE, A
REGEV, A
[J]. ADVANCES IN MATHEMATICS, 1987, 64 (02) : 118 - 175
[3] Lie subalgebras of differential operators on the super circle
Cheng, SJ
Wang, WQ
[J]. PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, 2003, 39 (03) : 545 - 600
[4] Howe duality and combinatorial character formula for orthosymplectic Lie superalgebras
Cheng, SJ
Zhang, RB
[J]. ADVANCES IN MATHEMATICS, 2004, 182 (01) : 124 - 172
[5] Howe duality for Lie superalgebras
Cheng, SJ
Wang, WQ
[J]. COMPOSITIO MATHEMATICA, 2001, 128 (01) : 55 - 94
[6] SYMPLECTIC STANDARD TABLEAUX
DECONCINI, C
[J]. ADVANCES IN MATHEMATICS, 1979, 34 (01) : 1 - 27
[7] Fulton W., 1997, YOUNG TABLEAUX, V35
[8] Hong J., 2002, GRADUATE STUDIES MAT, V42, DOI [10.1090/gsm/042, DOI 10.1090/GSM/042]
[9] Stable branching rules for classical symmetric pairs
Howe, R
Tan, EC
Willenbring, JF
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 357 (04) : 1601 - 1626
[10] REMARKS ON CLASSICAL INVARIANT-THEORY
HOWE, R
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1989, 313 (02) : 539 - 570

← 1 2 3 4 →