The Littlewood-Richardson rule for Schur $P$-, $Q$-multiple zeta functions
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918402019295232 |
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| author | Hanaki, Hikari |
| author_facet | Hanaki, Hikari |
| contents | The Schur $P$-, $Q$-multiple zeta functions were defined by Nakasuji and Takeda inspired by the tableau representation of Schur $P$-, $Q$-functions. While a product of two Schur $P$-functions expands as a linear combination of Schur $P$-functions, we obtain a similar expansion formula for the Schur $P$-multiple zeta functions by taking summation over the symmetric group permutating all the variables. We also introduce a expansion formula of skew Schur $Q$-multiple zeta functions by taking summation over the symmetric group. Furthermore, this skew type formula can be refined by restricting the symmetric group to its specific subgroup. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21480 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Littlewood-Richardson rule for Schur $P$-, $Q$-multiple zeta functions Hanaki, Hikari Number Theory 11M32, 05E05, 11M41 The Schur $P$-, $Q$-multiple zeta functions were defined by Nakasuji and Takeda inspired by the tableau representation of Schur $P$-, $Q$-functions. While a product of two Schur $P$-functions expands as a linear combination of Schur $P$-functions, we obtain a similar expansion formula for the Schur $P$-multiple zeta functions by taking summation over the symmetric group permutating all the variables. We also introduce a expansion formula of skew Schur $Q$-multiple zeta functions by taking summation over the symmetric group. Furthermore, this skew type formula can be refined by restricting the symmetric group to its specific subgroup. |
| title | The Littlewood-Richardson rule for Schur $P$-, $Q$-multiple zeta functions |
| topic | Number Theory 11M32, 05E05, 11M41 |
| url | https://arxiv.org/abs/2603.21480 |