On some noncommutative symmetric functions analogous to Hall-Littlewood and Macdonald polynomials

TL;DR

This paper explores noncommutative analogues of Hall-Littlewood and Macdonald polynomials, introducing new families of symmetric functions with parameter dependence, expanding the algebraic understanding of these objects.

Contribution

It defines novel noncommutative symmetric functions depending on two parameter sequences, linking existing polynomial analogues and expanding their algebraic framework.

Findings

New families of noncommutative symmetric functions introduced

Connections established between various noncommutative analogues

Parameter-dependent structures generalized in the noncommutative setting

Abstract

We investigate the connections between various noncommutative analogues of Hall-Littlewood and Macdonald polynomials, and define some new families of noncommutative symmetric functions depending on two sequences of parameters.