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Annals of Combinatorics

, Volume 20, Issue 4, pp 831–868 | Cite as

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

  • Jia HuangEmail author
Article

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.

Keywords

0-Hecke algebra tableau ribbon Grothendieck group quasisymmetric function noncommutative symmetric function type B type D antipode skew element 

Mathematics Subject Classification

05E05 05E10 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of Nebraska at KearneyKearneyUSA

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