Products of two involutions in orthogonal and symplectic groups

DOI10.1007/s10711-023-00845-4zbMath1528.15011arXiv2302.00501OpenAlexW4387671207MaRDI QIDQ6082236

Clément de Seguins Pazzis

Publication date: 3 November 2023

Published in: Geometriae Dedicata (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2302.00501

zbMATH Keywords

symplectic groupdecompositionorthogonal groupinvolutioncanonical formWall invariants

Mathematics Subject Classification ID

Factorization of matrices (15A23) Vector and tensor algebra, theory of invariants (15A72) General properties and structure of complex Lie groups (22E10) Quadratic and bilinear forms, inner products (15A63) Canonical forms, reductions, classification (15A21) Orthogonal matrices (15B10)

Related Items (1)

The quadratic sum problem for symplectic pairs

Cites Work

• Each symplectic matrix is a product of four symplectic involutions
• Products of two involutions in classical groups of characteristic 2
• Paare alternierender Formen
• Products of involutions
• The sum and the product of two quadratic matrices: regular cases
• Every real symplectic matrix is a product of real symplectic involutions
• Generation of the symplectic group by involutions
• Products of involutions in the stable general linear group
• Product of two involutions
• The sum of two quadratic matrices: exceptional cases
• The product of two invertible quadratic matrices: exceptional cases
• A note on sums of three square-zero matrices
• On the conjugacy classes in the unitary, symplectic and orthogonal groups
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