Class expansion of some symmetric functions in Jucys-Murphy elements

TL;DR

This paper introduces a method to compute the class expansion of symmetric functions in Jucys-Murphy elements, with a focus on Hall-Littlewood functions that interpolate between key symmetric functions.

Contribution

The paper develops a novel computational method for class expansion of symmetric functions in Jucys-Murphy elements, specifically applied to Hall-Littlewood functions.

Findings

Method successfully computes class expansions for Hall-Littlewood functions.

Provides insights into the structure of symmetric functions in Jucys-Murphy elements.

Bridges power sum and complete symmetric functions through interpolation.

Abstract

We present a method to compute the class expansion of a symmetric function in the Jucys-Murphy elements of the symmetric group. We apply this method to one-row Hall-Littlewood symmetric functions, which interpolate between power sums and complete symmetric functions.