Tensor decomposition of Demazure crystals for symmetrizable Kac-Moody Lie algebras
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912849795743744 |
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| author | Setia, Divya |
| author_facet | Setia, Divya |
| contents | We study the tensor product of Demazure crystals for symmetrizable Kac-Moody Lie algebras. It is not necessary that the tensor product of Demazure crystals is isomorphic to a disjoint union of Demazure crystals. In this paper, we provide necessary and sufficient conditions for the decomposition of the tensor product of Demazure crystals as a disjoint union of Demazure crystals. Our results are the generalization of the results proved by Anthony Joseph and Takafumi Kouno. As an application, we obtain a sufficient condition when the product of Demazure characters is a linear combination of Demazure characters with nonnegative integer coefficients. In particular, we obtain a partial solution for the key positivity problem. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_18484 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tensor decomposition of Demazure crystals for symmetrizable Kac-Moody Lie algebras Setia, Divya Representation Theory Combinatorics 17B37, 17B10, 05E10 We study the tensor product of Demazure crystals for symmetrizable Kac-Moody Lie algebras. It is not necessary that the tensor product of Demazure crystals is isomorphic to a disjoint union of Demazure crystals. In this paper, we provide necessary and sufficient conditions for the decomposition of the tensor product of Demazure crystals as a disjoint union of Demazure crystals. Our results are the generalization of the results proved by Anthony Joseph and Takafumi Kouno. As an application, we obtain a sufficient condition when the product of Demazure characters is a linear combination of Demazure characters with nonnegative integer coefficients. In particular, we obtain a partial solution for the key positivity problem. |
| title | Tensor decomposition of Demazure crystals for symmetrizable Kac-Moody Lie algebras |
| topic | Representation Theory Combinatorics 17B37, 17B10, 05E10 |
| url | https://arxiv.org/abs/2601.18484 |