Checkerboard style Schur multiple zeta values and odd single zeta values

TL;DR

This paper introduces explicit formulas for Schur multiple zeta values, generalizing multiple zeta values, and reveals new sum representations for odd single zeta values using Checkerboard-style Young tableaux.

Contribution

It provides explicit formulas for Schur multiple zeta values and connects them to odd zeta values through novel sum representations and determinant formulas.

Findings

New sum representations for odd zeta values.

Determinant formulas involving odd zeta values.

Explicit formulas for Schur multiple zeta values.

Abstract

We give explicit formulas for the recently introduced Schur multiple zeta values, which generalize multiple zeta(-star) values and which assign to a Young tableaux a real number. In this note we consider Young tableaux of various shapes, filled with alternating entries like a Checkerboard. In particular we obtain new sum representation for odd single zeta values in terms of these Schur multiple zeta values. As a special case we show that some Schur multiple zeta values of Checkerboard style, filled with 1 and 3, are given by determinants of matrices with odd single zeta values as entries.