Gelfand-Tsetlin Crystals of Kostant-Kumar modules
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916529801527296 |
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| author | Kushwaha, Mrigendra Singh |
| author_facet | Kushwaha, Mrigendra Singh |
| contents | We give Gelfand-Tsetlin crystals for the Kostant-Kumar modules for the finite simple Lie algebra of type A. Kostant-Kumar modules are cyclic submodules of the tensor product of two irreducible highest weight modules of a symmetrizable Kac-Moody Lie algebras. In this case (type A), we also provide a polytopal model for Kostant-Kumar modules in terms of BiKogan faces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13659 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Gelfand-Tsetlin Crystals of Kostant-Kumar modules Kushwaha, Mrigendra Singh Representation Theory Combinatorics 17B67, 17B10, 05E10 We give Gelfand-Tsetlin crystals for the Kostant-Kumar modules for the finite simple Lie algebra of type A. Kostant-Kumar modules are cyclic submodules of the tensor product of two irreducible highest weight modules of a symmetrizable Kac-Moody Lie algebras. In this case (type A), we also provide a polytopal model for Kostant-Kumar modules in terms of BiKogan faces. |
| title | Gelfand-Tsetlin Crystals of Kostant-Kumar modules |
| topic | Representation Theory Combinatorics 17B67, 17B10, 05E10 |
| url | https://arxiv.org/abs/2412.13659 |