The Pieri formulas for hook type Schur multiple zeta functions

TL;DR

This paper develops Pieri formulas for hook type Schur multiple zeta functions, introducing a new insertion rule for Young tableaux and proving extended Jacobi-Trudi formulas to establish these results.

Contribution

It introduces a novel insertion rule and extends Jacobi-Trudi formulas to Schur multiple zeta functions of hook type, advancing the combinatorial understanding of these functions.

Findings

Established Pieri formulas for hook type Schur multiple zeta functions

Developed a new insertion rule for Young tableaux

Proved extended Jacobi-Trudi formulas for these functions

Abstract

We study the Pieri type formulas for the Schur multiple zeta functions along with those for the Schur polynomials. To formulate these formulas, we introduce a new insertion rule for adding boxes in the Young tableaux and obtain the results for the hook type Schur multiple zeta functions. For the proof, we show {certain} extended Jacobi-Trudi formulas for the Schur multiple zeta functions.