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

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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

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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