Hecke combinatorics, Kåhrstr{ö}m's conditions and Kostant's problem
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911641750208512 |
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| author | Creedon, Samuel Mazorchuk, Volodymyr |
| author_facet | Creedon, Samuel Mazorchuk, Volodymyr |
| contents | This paper discusses various aspects of the Hecke algebra combinatorics that are related to conditions appearing in Kåhrstr{ö}m's conjecture that addresses Kostant's problem for simple highest weight modules in the Bernstein-Gelfand-Gelfand category $\mathcal{O}$ for the complex Lie algebra $\mathfrak{sl}_n$. In particular, we study cyclic submodules of the regular Hecke module that are generated by the elements of the (dual) Kazhdan-Lusztig basis as well as the problem of left cell invariance for both categorical and combinatorial Kåhrstr{ö}m's conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05817 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hecke combinatorics, Kåhrstr{ö}m's conditions and Kostant's problem Creedon, Samuel Mazorchuk, Volodymyr Representation Theory This paper discusses various aspects of the Hecke algebra combinatorics that are related to conditions appearing in Kåhrstr{ö}m's conjecture that addresses Kostant's problem for simple highest weight modules in the Bernstein-Gelfand-Gelfand category $\mathcal{O}$ for the complex Lie algebra $\mathfrak{sl}_n$. In particular, we study cyclic submodules of the regular Hecke module that are generated by the elements of the (dual) Kazhdan-Lusztig basis as well as the problem of left cell invariance for both categorical and combinatorial Kåhrstr{ö}m's conditions. |
| title | Hecke combinatorics, Kåhrstr{ö}m's conditions and Kostant's problem |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2510.05817 |