Algebras and Representation Theory

, Volume 20, Issue 2, pp 379–431 | Cite as

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.

Keywords

Representation of categories Free quasisymmetric function Quasisymmetric function Noncomutative symmetric function Symmetric function Malvenuto–Reutenauer algebra Descent algebra 0-Hecke algebra Induction Restriction Coxeter group Type B type D 

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© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

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

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