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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Nebraska at Kearney, Kearney, NE, 68849, USA

    Jia Huang

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  1. Jia Huang
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Correspondence to Jia Huang.

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The author thanks Victor Reiner for helpful conversations and encouragement.

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Huang, J. A Tableau Approach to the Representation Theory of 0-Hecke Algebras. Ann. Comb. 20, 831–868 (2016). https://doi.org/10.1007/s00026-016-0338-5

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  • DOI: https://doi.org/10.1007/s00026-016-0338-5

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