Polynomial Representations of the Hecke Algebra of the Symmetric Group

Lascoux, Alain

doi:10.1142/s0218196713400109

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

Huang

2016

Ann. Comb.

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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 type B and D, and obtain a correspondence between the representation theory of 0-Hecke algebras of type B and D and quasisymmetric functions and noncommutative symmetric functions of type B and D. Other applications are also provided.

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