Shuffle product formula of the Schur multiple zeta values of hook type

TL;DR

This paper establishes a shuffle product formula for Schur multiple zeta values of hook type, introducing new poset structures and a modified zeta function to generalize and compute their products explicitly.

Contribution

It introduces 2-labeled Schur posets and a modified Hurwitz-type Schur multiple zeta function to derive an explicit shuffle product formula for hook-type Schur multiple zeta values.

Findings

Derived explicit shuffle product formula for hook-type Schur multiple zeta values.

Introduced 2-labeled Schur posets to generalize integral expressions.

Defined elementary factorial Schur multiple zeta function for product calculations.

Abstract

We discuss the shuffle product of the Schur multiple zeta values, which are the special values of Schur multiple zeta functions. We first define $2$-labeled Schur posets to generalize Yamamoto's integral expression of the multiple zeta values and consider the product of hook-type Schur multiple zeta values by using these posets. Then, for the derived terms, we introduce a modified Hurwitz-type Schur multiple zeta function of hook type, named an elementary factorial Schur multiple zeta function. Furthermore, we generalize $2$-labeled Schur posets to consider the shuffle product of the elementary factorial Schur multiple zeta values and obtain an explicit formula for their shuffle product.