The Littlewood-Richardson rule for Schur multiple zeta functions

TL;DR

This paper extends the understanding of Schur multiple zeta functions by deriving a refined product formula that involves summation over a specific subgroup of permutations, inspired by the classical Littlewood-Richardson rule.

Contribution

It introduces a new, more precise formula for the product of Schur multiple zeta functions, refining previous symmetrization approaches.

Findings

Derived a refined product formula for Schur multiple zeta functions

Connected the formula to subgroup restrictions of the symmetric group

Enhanced the algebraic understanding of Schur multiple zeta functions

Abstract

The Schur multiple zeta function was defined as a multivariable function by Nakasuji-Phuksuwan-Yamasaki. Inspired by the product formula of Schur functions, the products of Schur multiple zeta functions have been studied. While the product of two Schur functions expands as a linear combination of Schur functions, it is known that a similar expansion for the product of Schur multiple zeta functions can be obtained by symmetrizing, i.e., by taking the summation over all permutations of the variables. In this paper, we present a more refined formula by restricting the summation from the full symmetric group to its specific subgroup.