Orbits of groups generated by transvections over $\FF_2$
Algebraic Geometry
2007-05-23 v2 Combinatorics
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.
Cite
@article{arxiv.math/0303098,
title = {Orbits of groups generated by transvections over $\FF_2$},
author = {Ahmet Seven},
journal= {arXiv preprint arXiv:math/0303098},
year = {2007}
}
Comments
LaTeX, 23 pages, 25 figures. Substantial revision: new theorems and references added