A Uniform Generalization of Some Combinatorial Hopf Algebras

Jia Huang

doi:10.1007/s10468-016-9648-x

A Uniform Generalization of Some Combinatorial Hopf Algebras

Jia Huang

Mathematics and Statistics

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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 language	English (US)
Pages (from-to)	379-431
Number of pages	53
Journal	Algebras and Representation Theory
Volume	20
Issue number	2
DOIs	https://doi.org/10.1007/s10468-016-9648-x
State	Published - Apr 1 2017

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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10.1007/s10468-016-9648-x

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AB - 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.

KW - 0-Hecke algebra

KW - Coxeter group

KW - Descent algebra

KW - Free quasisymmetric function

KW - Induction

KW - Malvenuto–Reutenauer algebra

KW - Noncomutative symmetric function

KW - Quasisymmetric function

KW - Representation of categories

KW - Restriction

KW - Symmetric function

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A Uniform Generalization of Some Combinatorial Hopf Algebras

Abstract

Keywords

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