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.

Original languageEnglish (US)
Pages (from-to)379-431
Number of pages53
JournalAlgebras and Representation Theory
Volume20
Issue number2
DOIs
Publication statusPublished - Apr 1 2017

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Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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