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arXiv · 2208.11909

Symmetric Schur multiple zeta functions

Maki Nakasuji·Wataru Takeda
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Abstract

We introduce the multiple zeta functions with structures similar to those of symmetric functions such as Schur $P$-, Schur $Q$-, symplectic and orthogonal functions in the representation theory. We first consider their basic properties such as a domain of absolute convergence. And then by restricting to the truncated multiple zeta functions, we obtain the pfaffian expression of the Schur $Q$-multiple zeta functions, the sum formula for Schur $P$- and Schur $Q$-multiple zeta functions, the determinant expressions of symplectic and orthogonal Schur multiple zeta functions under an assumption on variables. Finally, we generalize those to the quasi-symmetric functions.

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Maki Nakasuji, Wataru Takeda. 2022-08-25. Symmetric Schur multiple zeta functions. https://doi.org/10.4153/s0008414x25000203

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