Expressions of content-parametrized Schur multiple zeta-functions via the Giambelli formula

TL;DR

This paper derives explicit formulas for content-parametrized Schur multiple zeta-functions using the Giambelli formula, connecting them to Euler-Zagier type multiple zeta-functions and their variants.

Contribution

It introduces a method to express general content-parametrized Schur multiple zeta-functions via the Giambelli formula, extending previous results for hook types.

Findings

Explicit formulas for hook-type Schur multiple zeta-functions.

General expressions for content-parametrized Schur multiple zeta-functions.

Connections to Euler-Zagier multiple zeta-functions and root system variants.

Abstract

In this article, we consider the expressions for content-parametrized Schur multiple zeta-functions in terms of multiple zeta-functions of Euler-Zagier type and their star-variants, or in terms of modified zeta-functions of root systems. First of all, we focus on the Schur multiple zeta-function of hook type. And then, applying the Giambelli formula and induction argument, we obtain the expressions for general content-parametrized Schur multiple zeta-functions.