A uniform generalization of some combinatorial Hopf algebras

2015/06/09 by Huang, Jia
#05E05 #05E10 #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1506.02962

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 all 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.

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