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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.15837 |
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| _version_ | 1866912540304343040 |
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| author | Biswal, Rekha Gaussent, Stéphane |
| author_facet | Biswal, Rekha Gaussent, Stéphane |
| contents | In this paper, using crystal theory we prove the existence of a new family of irreducible components appearing in the tensor product of two irreducible integrable highest weight modules over symmetrizable Kac-Moody algebras motivated by the Schur positivity conjecture, Kostant conjecture and Wahl conjecture. We also prove Schur positivity conjecture in full generality when the Lie algebra is a simple Lie algebra under the assumption that $λ> > μ$, i.e. if $λ$ and $μ$ are the two dominant weights appearing in the tensor product then $λ+wμ$ is a dominant weight for all the Weyl group elements $w$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15837 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of a new family of irreducible components in the tensor product and its applications Biswal, Rekha Gaussent, Stéphane Representation Theory In this paper, using crystal theory we prove the existence of a new family of irreducible components appearing in the tensor product of two irreducible integrable highest weight modules over symmetrizable Kac-Moody algebras motivated by the Schur positivity conjecture, Kostant conjecture and Wahl conjecture. We also prove Schur positivity conjecture in full generality when the Lie algebra is a simple Lie algebra under the assumption that $λ> > μ$, i.e. if $λ$ and $μ$ are the two dominant weights appearing in the tensor product then $λ+wμ$ is a dominant weight for all the Weyl group elements $w$. |
| title | Existence of a new family of irreducible components in the tensor product and its applications |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2501.15837 |