Noncommutative symmetric functions and quasi-symmetric functions with two and more paramters

TL;DR

This paper introduces two-parameter families of noncommutative symmetric and quasi-symmetric functions, serving as analogues to Macdonald symmetric functions in noncommutative settings.

Contribution

It defines new two-parameter noncommutative symmetric and quasi-symmetric functions, extending the classical Macdonald functions to noncommutative frameworks.

Findings

Two-parameter families generalize classical symmetric functions.

Analogues of Macdonald functions are constructed in noncommutative settings.

Potential applications in algebraic combinatorics and representation theory.

Abstract

We define two-parameter families of noncommutative symmetric functions and quasi-symmetric functions, which appear to be the proper analogues of the Macdonald symmetric functions in these settings.