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) |
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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 |
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)