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A Uniform Generalization of Some Combinatorial Hopf Algebras

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Abstract

We generalize the Hopf algebras of free quasisymmetric functions, quasisymmetric functions, noncommutative symmetric functions, and symmetric functions to certain representations of the category of finite Coxeter systems and its dual category. We investigate their connections with the representation theory of 0-Hecke algebras of finite Coxeter systems. Restricted to type B and D we obtain dual graded modules and comodules over the corresponding Hopf algebras in type A.

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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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Presented by Anne Schilling.

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Huang, J. A Uniform Generalization of Some Combinatorial Hopf Algebras. Algebr Represent Theor 20, 379–431 (2017). https://doi.org/10.1007/s10468-016-9648-x

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  • DOI: https://doi.org/10.1007/s10468-016-9648-x

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