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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.01699 |
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| _version_ | 1866917588299153408 |
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| author | Fresse, Lucas Mehdi, Salah |
| author_facet | Fresse, Lucas Mehdi, Salah |
| contents | We obtain inductive and enumerative formulas for the multiplicities of the weights of the spin module for the Clifford algebra of a Levi subalgebra in a complex semisimple Lie algebra. Our formulas involve only matrices and tableaux, and our techniques combine linear algebra, Lie theory, and combinatorics. Moreover, this suggests a relationship with complex nilpotent orbits. The case of the special linear Lie algebra $\mathfrak{sl}(n,{\mathbb C})$ is emphasized. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_01699 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Matrix formulas for multiplicities in the spin module Fresse, Lucas Mehdi, Salah Representation Theory We obtain inductive and enumerative formulas for the multiplicities of the weights of the spin module for the Clifford algebra of a Levi subalgebra in a complex semisimple Lie algebra. Our formulas involve only matrices and tableaux, and our techniques combine linear algebra, Lie theory, and combinatorics. Moreover, this suggests a relationship with complex nilpotent orbits. The case of the special linear Lie algebra $\mathfrak{sl}(n,{\mathbb C})$ is emphasized. |
| title | Matrix formulas for multiplicities in the spin module |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2304.01699 |