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