A general framework for the polynomiality property of the structure coefficients of double-class algebras

Omar Tout

doi:10.1007/s10801-017-0736-8

A general framework for the polynomiality property of the structure coefficients of double-class algebras

Omar Tout^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

In this paper, we build a general framework in which we give a formula that shows the form of the structure coefficients of double-class algebras and centers of group algebras. This formula allows us to give a polynomiality property for the structure coefficients of some important algebras. In particular, we re-obtain the polynomiality property of the structure coefficients in the cases of the center of the symmetric group algebra and the Hecke algebra of the pair (S₂ _n, B_n). We also assign a new polynomiality property for the structure coefficients of the center of the hyperoctahedral group algebra and the Hecke algebra of the pair (Sn×Sn-1opp,diag(Sn-1)).

Original language	English
Pages (from-to)	1111-1152
Number of pages	42
Journal	Journal of Algebraic Combinatorics
Volume	45
Issue number	4
DOIs	https://doi.org/10.1007/s10801-017-0736-8
Publication status	Published - Jun 1 2017

Keywords

Center of the hyperoctahedral group algebra
Centers of group algebras
Double-class algebras
Hecke algebra of the pair(S × S , diag(S))
Polynomiality property of the structure coefficients
Structure coefficients

ASJC Scopus subject areas

Algebra and Number Theory
Discrete Mathematics and Combinatorics

Access to Document

10.1007/s10801-017-0736-8

Cite this

@article{05934e27a7a64b2aa0d099e0641c16ee,

title = "A general framework for the polynomiality property of the structure coefficients of double-class algebras",

abstract = "In this paper, we build a general framework in which we give a formula that shows the form of the structure coefficients of double-class algebras and centers of group algebras. This formula allows us to give a polynomiality property for the structure coefficients of some important algebras. In particular, we re-obtain the polynomiality property of the structure coefficients in the cases of the center of the symmetric group algebra and the Hecke algebra of the pair (S2 n, Bn). We also assign a new polynomiality property for the structure coefficients of the center of the hyperoctahedral group algebra and the Hecke algebra of the pair (Sn×Sn-1opp,diag(Sn-1)).",

keywords = "Center of the hyperoctahedral group algebra, Centers of group algebras, Double-class algebras, Hecke algebra of the pair(S × S , diag(S)), Polynomiality property of the structure coefficients, Structure coefficients",

author = "Omar Tout",

note = "Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media New York.",

year = "2017",

month = jun,

day = "1",

doi = "10.1007/s10801-017-0736-8",

language = "English",

volume = "45",

pages = "1111--1152",

journal = "Journal of Algebraic Combinatorics",

issn = "0925-9899",

publisher = "Springer Netherlands",

number = "4",

}

TY - JOUR

T1 - A general framework for the polynomiality property of the structure coefficients of double-class algebras

AU - Tout, Omar

PY - 2017/6/1

Y1 - 2017/6/1

N2 - In this paper, we build a general framework in which we give a formula that shows the form of the structure coefficients of double-class algebras and centers of group algebras. This formula allows us to give a polynomiality property for the structure coefficients of some important algebras. In particular, we re-obtain the polynomiality property of the structure coefficients in the cases of the center of the symmetric group algebra and the Hecke algebra of the pair (S2 n, Bn). We also assign a new polynomiality property for the structure coefficients of the center of the hyperoctahedral group algebra and the Hecke algebra of the pair (Sn×Sn-1opp,diag(Sn-1)).

AB - In this paper, we build a general framework in which we give a formula that shows the form of the structure coefficients of double-class algebras and centers of group algebras. This formula allows us to give a polynomiality property for the structure coefficients of some important algebras. In particular, we re-obtain the polynomiality property of the structure coefficients in the cases of the center of the symmetric group algebra and the Hecke algebra of the pair (S2 n, Bn). We also assign a new polynomiality property for the structure coefficients of the center of the hyperoctahedral group algebra and the Hecke algebra of the pair (Sn×Sn-1opp,diag(Sn-1)).

KW - Center of the hyperoctahedral group algebra

KW - Centers of group algebras

KW - Double-class algebras

KW - Hecke algebra of the pair(S × S , diag(S))

KW - Polynomiality property of the structure coefficients

KW - Structure coefficients

UR - http://www.scopus.com/inward/record.url?scp=85015634419&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85015634419&partnerID=8YFLogxK

U2 - 10.1007/s10801-017-0736-8

DO - 10.1007/s10801-017-0736-8

M3 - Article

AN - SCOPUS:85015634419

SN - 0925-9899

VL - 45

SP - 1111

EP - 1152

JO - Journal of Algebraic Combinatorics

JF - Journal of Algebraic Combinatorics

IS - 4

ER -

A general framework for the polynomiality property of the structure coefficients of double-class algebras

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this