Super-immanants and Littlewood correspondences
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866908906973822976 |
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| author | Jing, Naihuan Liu, Yinlong Zhang, Jian |
| author_facet | Jing, Naihuan Liu, Yinlong Zhang, Jian |
| contents | In this paper, we introduce the notion of super-immanants for supermatrices over a supercommutative algebra. Using the super Schur-Weyl duality we show that the super immanants play a significant role in covariant tensor representations of the general linear Lie superalgebra. Among various things, we obtain a supertrace formula for super-immanants, which generalizes Kostant's trace formula to the super setting. Furthermore, we show that the Littlewood correspondences between super-immanants and supersymmetric polynomials establish an isomorphism between their corresponding algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21893 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Super-immanants and Littlewood correspondences Jing, Naihuan Liu, Yinlong Zhang, Jian Representation Theory Combinatorics Quantum Algebra Primary: 17A70 Secondary: 17B35, 15A15, 05E05, 05E10 In this paper, we introduce the notion of super-immanants for supermatrices over a supercommutative algebra. Using the super Schur-Weyl duality we show that the super immanants play a significant role in covariant tensor representations of the general linear Lie superalgebra. Among various things, we obtain a supertrace formula for super-immanants, which generalizes Kostant's trace formula to the super setting. Furthermore, we show that the Littlewood correspondences between super-immanants and supersymmetric polynomials establish an isomorphism between their corresponding algebras. |
| title | Super-immanants and Littlewood correspondences |
| topic | Representation Theory Combinatorics Quantum Algebra Primary: 17A70 Secondary: 17B35, 15A15, 05E05, 05E10 |
| url | https://arxiv.org/abs/2603.21893 |