### 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 | |

State | Published - 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)

### Cite this

**A Uniform Generalization of Some Combinatorial Hopf Algebras.** / Huang, Jia.

Research output: Contribution to journal › Article

*Algebras and Representation Theory*, vol. 20, no. 2, pp. 379-431. https://doi.org/10.1007/s10468-016-9648-x

}

TY - JOUR

T1 - A Uniform Generalization of Some Combinatorial Hopf Algebras

AU - Huang, Jia

PY - 2017/4/1

Y1 - 2017/4/1

N2 - 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.

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

KW - Type B

KW - type D

UR - http://www.scopus.com/inward/record.url?scp=84990934099&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990934099&partnerID=8YFLogxK

U2 - 10.1007/s10468-016-9648-x

DO - 10.1007/s10468-016-9648-x

M3 - Article

AN - SCOPUS:84990934099

VL - 20

SP - 379

EP - 431

JO - Algebras and Representation Theory

JF - Algebras and Representation Theory

SN - 1386-923X

IS - 2

ER -