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Main Author: Nebe, Gabriele
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2409.16926
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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