Canonical matrices of forms and pairs of forms over finite and p-adic fields

2010/11/13 by Vladimir V. Sergeichuk, Sergeichuk, Vladimir V.
Mathematics · #15A21 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Representation Theory (math.RT) #advanced mathematical theories #math.RT #msc:15A21

paper · pdf · doi:10.48550/arxiv.1011.3142

41 pages

arxiv created 2010/11/13 · openalex publication_date 2010/11/13 · arxiv updated 2010/11/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Canonical matrices of (a) bilinear and sesquilinear forms, (b) pairs of forms, in which every form is symmetric or skew-symmetric, and (c) pairs of Hermitian forms are given over finite fields of characteristic not 2 and over finite extensions of the field Q_p of p-adic numbers with p not 2. These canonical matrices are special cases of the canonical matrices of (a)-(c) over a field of characteristic not 2 that were obtained in [V. V. Sergeichuk, Math. USSR-Izv. 31 (1988) 481-501] up to classification of quadratic or Hermitian forms over its finite extensions.

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