Orbits of groups generated by transvections over F-2


Creative Commons License

Seven A. İ.

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

  • Publication Type: Article / Article
  • Volume: 21 Issue: 4
  • Publication Date: 2005
  • Doi Number: 10.1007/s10801-005-3021-1
  • Title of Journal : JOURNAL OF ALGEBRAIC COMBINATORICS
  • Page Numbers: pp.449-474

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.