Orbits of groups generated by transvections over $\FF_2$

Details Orbits of groups generated by transvections over $\FF_2$ Orbits of groups generated by transvections over $\FF_2$

2003-03-07

arxiv.org/abs/math/0303098v2

Mathematics

Algebraic Geometry

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

Scientific paper

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.

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