Work

Symmetrizations of quadratic and Hermitian forms

Year: 2025

Type: article

Abstract: 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), $$(1^n)$$ ( 1 n ) , $$(2,1^{n-2})$$ ( 2 , 1 n - 2 ) and $$(3,1^{n-3})$$ ( 3 , 1 n - 3 ) as well as for all partitions of $$n\le 7$$ n ≤ 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.

Source: Journal of Algebraic Combinatorics

DOI: 10.1007/s10801-025-01399-2

Author: Gabriele Nebe

Institution: RWTH Aachen University

Language: English

Topic: Advanced Combinatorial Mathematics

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funder: RWTH Aachen University