An interpolation of the generalized duality formula for the Schur multiple zeta values to complex functions

TL;DR

This paper extends the duality and Ohno relations for Schur multiple zeta functions to complex arguments, providing a broader understanding of their functional equations and linear relations.

Contribution

It introduces an interpolation of the generalized duality formula for Schur multiple zeta values to complex functions, expanding the scope of known relations.

Findings

The Ohno relation for Schur multiple zeta values holds for complex numbers.

The paper generalizes duality formulas to complex arguments.

It advances the understanding of linear relations among Schur multiple zeta functions.

Abstract

One of the important research subjects in the study of multiple zeta functions is to clarify the linear relations and functional equations among them. The Schur multiple zeta functions are a generalization of the multiple zeta functions of Euler-Zagier type. Among many relations, the duality formula and its generalization are important families for both Euler-Zagier type and Schur type multiple zeta values. In this paper, following the method of previous works for multiple zeta values of Euler-Zagier type, we give an interpolation of the sums in the generalized duality formula, called Ohno relation, for Schur multiple zeta values. Moreover, we prove that the Ohno relation for Schur multiple zeta values is valid for complex numbers.