The $q$-immanants and higher quantum Capelli identities
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909565798318080 |
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| author | Jing, Naihuan Liu, Ming Molev, Alexander |
| author_facet | Jing, Naihuan Liu, Ming Molev, Alexander |
| contents | We construct polynomials ${\mathbb{S}}_μ(z)$ parameterized by Young diagrams $μ$, whose coefficients are central elements of the quantized enveloping algebra ${\rm U}_q({\mathfrak{gl}}_n)$. Their constant terms coincide with the central elements provided by the general construction of Drinfeld and Reshetikhin. For another special value of $z$, we get $q$-analogues of Okounkov's quantum immanants for ${\mathfrak{gl}}_n$. We show that the Harish-Chandra image of ${\mathbb{S}}_μ(z)$ is a factorial Schur polynomial. We also prove quantum analogues of the higher Capelli identities and derive Newton-type identities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_09855 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The $q$-immanants and higher quantum Capelli identities Jing, Naihuan Liu, Ming Molev, Alexander Quantum Algebra Representation Theory We construct polynomials ${\mathbb{S}}_μ(z)$ parameterized by Young diagrams $μ$, whose coefficients are central elements of the quantized enveloping algebra ${\rm U}_q({\mathfrak{gl}}_n)$. Their constant terms coincide with the central elements provided by the general construction of Drinfeld and Reshetikhin. For another special value of $z$, we get $q$-analogues of Okounkov's quantum immanants for ${\mathfrak{gl}}_n$. We show that the Harish-Chandra image of ${\mathbb{S}}_μ(z)$ is a factorial Schur polynomial. We also prove quantum analogues of the higher Capelli identities and derive Newton-type identities. |
| title | The $q$-immanants and higher quantum Capelli identities |
| topic | Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2408.09855 |