Geodesic
Orbits of groups generated by transvections over $\bbfF_2$.
Journal of Algebraic Combinatorics, Tome 21 (2005) no. 4, pp. 449-474.

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Summary: 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.
Keywords: keywords transvections, real double Bruhat cells 
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     author = {Seven, Ahmet I.},
     title = {Orbits of groups generated by transvections over $\bbfF_2$.},
     journal = {Journal of Algebraic Combinatorics},
     pages = {449--474},
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     number = {4},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JAC_2005__21_4_a0/}
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Seven, Ahmet I. Orbits of groups generated by transvections over $\bbfF_2$.. Journal of Algebraic Combinatorics, Tome 21 (2005) no. 4, pp. 449-474. http://geodesic.mathdoc.fr/item/JAC_2005__21_4_a0/