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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.16926 |
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| _version_ | 1866929515126587392 |
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| author | Nebe, Gabriele |
| author_facet | Nebe, Gabriele |
| contents | The paper develops elementary linear algebra methods to compute the determinants of the tensor symmetrizations of quadratic and hermitian forms over fields of good characteristic. Explicit results are given for the partitions $(n)$, $(1^n)$, $(2,1^{n-2})$ and $(3,1^{n-3})$ as well as for all partitions of $n\leq 7$. For orthogonal groups these symmetrizations are not irreducible and we continue to find the determinants of their irreducible constituents, the refined symmetrizations, over fields of characteristic 0. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_16926 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetrizations of quadratic and hermitian forms Nebe, Gabriele Combinatorics Number Theory Representation Theory 20C15, 11E12 The paper develops elementary linear algebra methods to compute the determinants of the tensor symmetrizations of quadratic and hermitian forms over fields of good characteristic. Explicit results are given for the partitions $(n)$, $(1^n)$, $(2,1^{n-2})$ and $(3,1^{n-3})$ as well as for all partitions of $n\leq 7$. For orthogonal groups these symmetrizations are not irreducible and we continue to find the determinants of their irreducible constituents, the refined symmetrizations, over fields of characteristic 0. |
| title | Symmetrizations of quadratic and hermitian forms |
| topic | Combinatorics Number Theory Representation Theory 20C15, 11E12 |
| url | https://arxiv.org/abs/2409.16926 |