On the algebraic decomposition of a centralizer algebra of the hyperoctahedral group

被引：0

作者：

Orellana, RC ^{[1
]}

机构：

[1] Dartmouth Coll, Dept Math, Hanover, NH 03755 USA

来源：

Algebraic Structures and Their Representations | 2005年 / 376卷

关键词：

centralizer algebra; partition algebra; hyperoctahedral group; coxeter group; bratteli diagram;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we give a combinatorial rule for the decomposition of tenser powers of the signed permutation representation of the hyperoctahedral group. We then use this rule to describe the Bratteli diagram of a centralizer algebra of this group over k-th tenser space. We show that a basis for this algebra can be described completely in terms of set partitions and we give a set of generators and relations.

引用

页码：345 / 357

页数：13

共 37 条

[21] The Hyperoctahedral Group, Symmetric Group Representations and the Moments of the Real Wishart Distribution [J].

P. Graczyk ;

G. Letac ;

H. Massam .

Journal of Theoretical Probability, 2005, 18 :1-42

[22] The hyperoctahedral group, symmetric group representations and the moments of the real Wishart distribution [J].

Graczyk, P ;

Letac, G ;

Massam, H .

JOURNAL OF THEORETICAL PROBABILITY, 2005, 18 (01) :1-42

[23] Centralizer algebras of the group associated to Z4-codes [J].

Kosuda, Masashi ;

Oura, Manabu .

DISCRETE MATHEMATICS, 2017, 340 (10) :2437-2446

[24] The Eulerian Distribution on the Involutions of the Hyperoctahedral Group is Indeed γ-Positive [J].

Cao, Jie ;

Liu, Lily Li .

GRAPHS AND COMBINATORICS, 2021, 37 (06) :1943-1951

[25] A linear portrayal of the Galois group G by the ring of irreducible characters of the hyperoctahedral group [J].

Cedric, Pemha Binyam Gabriel .

JOURNAL OF DISCRETE MATHEMATICAL SCIENCES & CRYPTOGRAPHY, 2025, 28 (03) :701-713

[26] The Eulerian distribution on the fixed-point free involutions of the hyperoctahedral group [J].

Jie Cao ;

Lily Li Liu .

Journal of Algebraic Combinatorics, 2023, 57 :793-810

[27] The Eulerian distribution on the fixed-point free involutions of the hyperoctahedral group [J].

Cao, Jie ;

Liu, Lily Li .

JOURNAL OF ALGEBRAIC COMBINATORICS, 2023, 57 (03) :793-810

[28] On the Centralizer Algebras of the Primitive Unitary Reflection Group of Order 96 [J].

Kosuda, Masashi ;

Oura, Manabu .

TOKYO JOURNAL OF MATHEMATICS, 2016, 39 (02) :469-482

[29] SPECHT MODULES AND SIMPLE MODULES FOR CENTRALIZER ALGEBRAS OF THE SYMMETRIC GROUP [J].

Dodge, Craig J. ;

Ellers, Harald .

COMMUNICATIONS IN ALGEBRA, 2016, 44 (02) :837-850

[30] On the decomposition matrix of the partition algebra in positive characteristic [J].

King, Oliver .

JOURNAL OF ALGEBRA, 2016, 451 :115-144

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