Orbits of groups generated by transvections over F-2

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Seven A. İ.

JOURNAL OF ALGEBRAIC COMBINATORICS, vol.21, no.4, pp.449-474, 2005 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 21 Issue: 4
  • Publication Date: 2005
  • Doi Number: 10.1007/s10801-005-3021-1
  • Journal Name: JOURNAL OF ALGEBRAIC COMBINATORICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.449-474
  • Keywords: transvections, real double Bruhat cells, DOUBLE BRUHAT CELLS, LIE-ALGEBRAS, GRAPHS
  • Middle East Technical University Affiliated: Yes

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. n 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.