Generalized Jacobi-Trudi determinants and evaluations of Schur multiple zeta values

TL;DR

This paper introduces new determinant formulas for Schur multiple zeta values, generalizing classical identities, and demonstrates their use in expressing certain Schur multiple zeta values as polynomials in Riemann zeta values, with shape-based conditions.

Contribution

It provides generalized Jacobi-Trudi determinant expressions for Schur multiple zeta values and characterizes when these values are polynomials in odd or even Riemann zeta values.

Findings

Schur multiple zeta values with alternating entries can be expressed as polynomials in Riemann zeta values.

Determinant formulas enable quick evaluation of specific Schur multiple zeta values.

Conditions on shape determine polynomial expressions in odd or even zeta values.

Abstract

We present new determinant expressions for regularized Schur multiple zeta values. These generalize the known Jacobi-Trudi formulae and can be used to quickly evaluate certain types of Schur multiple zeta values. Using these formulae we prove that every Schur multiple zeta value with alternating entries in 1 and 3 can be written as a polynomial in Riemann zeta values. Furthermore, we give conditions on the shape, which determine when such Schur multiple zetas are polynomials purely in odd or in even Riemann zeta values.