A Tableau Approach to the Representation Theory of 0-Hecke Algebras

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A 0-Hecke algebra is a deformation of the group algebra of a Coxeter group. Based on work of Norton and Krob-Thibon, we introduce a tableau approach to the representation theory of 0-Hecke algebras of type A, which resembles the classic approach to the representation theory of symmetric groups by Young tableaux and tabloids. We extend this approach to types B and D, and obtain a correspondence between the representation theory of 0-Hecke algebras of types B and D and quasisymmetric functions and noncommutative symmetric functions of types B and D. Other applications are also provided.

Original languageEnglish (US)
Pages (from-to)831-868
Number of pages38
JournalAnnals of Combinatorics
Volume20
Issue number4
DOIs
StatePublished - Dec 1 2016

Fingerprint

Hecke Algebra
Tableau
Representation Theory
Noncommutative Symmetric Functions
Quasi-symmetric Functions
Young Tableaux
Coxeter Group
Group Algebra
Symmetric group
Correspondence

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

A Tableau Approach to the Representation Theory of 0-Hecke Algebras. / Huang, Jia.

In: Annals of Combinatorics, Vol. 20, No. 4, 01.12.2016, p. 831-868.

Research output: Contribution to journalArticle

@article{8608eeb49f21448b963c638bcbe90b7c,
title = "A Tableau Approach to the Representation Theory of 0-Hecke Algebras",
abstract = "A 0-Hecke algebra is a deformation of the group algebra of a Coxeter group. Based on work of Norton and Krob-Thibon, we introduce a tableau approach to the representation theory of 0-Hecke algebras of type A, which resembles the classic approach to the representation theory of symmetric groups by Young tableaux and tabloids. We extend this approach to types B and D, and obtain a correspondence between the representation theory of 0-Hecke algebras of types B and D and quasisymmetric functions and noncommutative symmetric functions of types B and D. Other applications are also provided.",
author = "Jia Huang",
year = "2016",
month = "12",
day = "1",
doi = "10.1007/s00026-016-0338-5",
language = "English (US)",
volume = "20",
pages = "831--868",
journal = "Annals of Combinatorics",
issn = "0218-0006",
publisher = "Birkhauser Verlag Basel",
number = "4",

}

TY - JOUR

T1 - A Tableau Approach to the Representation Theory of 0-Hecke Algebras

AU - Huang, Jia

PY - 2016/12/1

Y1 - 2016/12/1

N2 - A 0-Hecke algebra is a deformation of the group algebra of a Coxeter group. Based on work of Norton and Krob-Thibon, we introduce a tableau approach to the representation theory of 0-Hecke algebras of type A, which resembles the classic approach to the representation theory of symmetric groups by Young tableaux and tabloids. We extend this approach to types B and D, and obtain a correspondence between the representation theory of 0-Hecke algebras of types B and D and quasisymmetric functions and noncommutative symmetric functions of types B and D. Other applications are also provided.

AB - A 0-Hecke algebra is a deformation of the group algebra of a Coxeter group. Based on work of Norton and Krob-Thibon, we introduce a tableau approach to the representation theory of 0-Hecke algebras of type A, which resembles the classic approach to the representation theory of symmetric groups by Young tableaux and tabloids. We extend this approach to types B and D, and obtain a correspondence between the representation theory of 0-Hecke algebras of types B and D and quasisymmetric functions and noncommutative symmetric functions of types B and D. Other applications are also provided.

UR - http://www.scopus.com/inward/record.url?scp=84994097032&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994097032&partnerID=8YFLogxK

U2 - 10.1007/s00026-016-0338-5

DO - 10.1007/s00026-016-0338-5

M3 - Article

AN - SCOPUS:84994097032

VL - 20

SP - 831

EP - 868

JO - Annals of Combinatorics

JF - Annals of Combinatorics

SN - 0218-0006

IS - 4

ER -