Orbits of groups generated by transvections over \FF₂

2003/03/07 by Ahmet Seven, Seven, Ahmet · 2 citations
Mathematics · #05E15 #14N10 #20F55 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #math.AG #math.CO #msc:05E15 #msc:14N10 #msc:20F55

paper · pdf · doi:10.48550/arxiv.math/0303098

LaTeX, 23 pages, 25 figures. Substantial revision: new theorems and references added

openalex publication_date 2003/03/07 · arxiv created 2003/12/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let V be a finite dimensional vector space over the two element field. We compute orbits for the linear action of groups generated by transvections with respect to a certain class of bilinear forms on V. In particular, we compute orbits that are in bijection with connected components of real double Bruhat cells in semisimple groups, extending results of M.Gekhtman, B. Shapiro, M. Shapiro, A.Vainshtein and A. Zelevinsky.

Cited by

• Cluster algebras: notes for 2004 IMCC (Chonju, Korea, August 2004)
• Homotopy Type of Intersections of Real Bruhat Cells in Dimension 6

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