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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.

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