Eigenvalues of supersymmetric Shimura operators and interpolation polynomials
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866908468789641216 |
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| author | Sahi, Siddhartha Zhu, Songhao |
| author_facet | Sahi, Siddhartha Zhu, Songhao |
| contents | The Shimura operators are a certain distinguished basis for invariant differential operators on a Hermitian symmetric space. Answering a question of Shimura, Sahi and Zhang showed that the Harish-Chandra images of these operators are specializations of certain $BC$-symmetric interpolation polynomials that were defined by Okounkov. We consider the analogs of Shimura operators for the Hermitian symmetric superpair $(\mathfrak{g},\mathfrak{k})$ where $\mathfrak{g}= \mathfrak{gl}(2p|2q)$ and $\mathfrak{k}= \mathfrak{gl}(p|q)\oplus \mathfrak{gl}(p|q)$ and we prove their Harish-Chandra images are specializations of certain $BC$-supersymmetric interpolation polynomials introduced by Sergeev--Veselov. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_08661 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Eigenvalues of supersymmetric Shimura operators and interpolation polynomials Sahi, Siddhartha Zhu, Songhao Representation Theory Commutative Algebra 17B10, 17B60, 05E05, 05E10, 81Q60 The Shimura operators are a certain distinguished basis for invariant differential operators on a Hermitian symmetric space. Answering a question of Shimura, Sahi and Zhang showed that the Harish-Chandra images of these operators are specializations of certain $BC$-symmetric interpolation polynomials that were defined by Okounkov. We consider the analogs of Shimura operators for the Hermitian symmetric superpair $(\mathfrak{g},\mathfrak{k})$ where $\mathfrak{g}= \mathfrak{gl}(2p|2q)$ and $\mathfrak{k}= \mathfrak{gl}(p|q)\oplus \mathfrak{gl}(p|q)$ and we prove their Harish-Chandra images are specializations of certain $BC$-supersymmetric interpolation polynomials introduced by Sergeev--Veselov. |
| title | Eigenvalues of supersymmetric Shimura operators and interpolation polynomials |
| topic | Representation Theory Commutative Algebra 17B10, 17B60, 05E05, 05E10, 81Q60 |
| url | https://arxiv.org/abs/2312.08661 |