Duality formula and its generalization for Schur multiple zeta functions

TL;DR

This paper explores the duality formula and its generalization for Schur multiple zeta functions, extending fundamental relations known for multiple zeta values to a broader class of functions.

Contribution

It introduces duality and Ohno-type relations for Schur multiple zeta values, expanding the algebraic framework of multiple zeta functions.

Findings

Established duality formula for Schur multiple zeta values

Derived generalized duality (Ohno relation) for these values

Enhanced understanding of algebraic structure of Schur multiple zeta functions

Abstract

In the study on multiple zeta values, the duality formula is one of the families of basic relations and plays an important role in the investigation of algebraic structure of the space spanned by all multiple zeta values along with the generalized duality formula (so called Ohno relation) obtained by the second author. In this article, we will discuss them for the Schur multiple zeta values which are the values at positive integers of the Schur multiple zeta function introduced by the first author, O. Phukswan and Y. Yamasaki.