Symmetric Schur multiple zeta functions

2022/08/25 by Maki Nakasuji, Nakasuji, Maki, Wataru Takeda +1
Mathematics · #05E05 #11M32 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Inequalities and Applications #Number Theory (math.NT) #math.CO #math.NT #msc:05E05 #msc:11M32

paper · pdf · doi:10.48550/arxiv.2208.11909

33 pages

arxiv created 2022/08/25 · openalex publication_date 2022/08/25 · openalex created_date 2025/10/10 · arxiv updated 2026/07/30 · openalex updated_date 2026/08/02

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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