Geodesic
On refinements of the Bruhat decomposition
Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 75-100.

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This article gives an explicit description of refined Bruhat cells. This description allows for an analysis of their closure patterns as well as for the calculation of structure constants of the endomorphism algebra of Gelfand-Graev representations. Most of the results rely on ideas and methods developed by V. V. Deodhar [Invent. Math. 79, 499--511 (1985; Zbl 0563.14023)] and C. W. Curtis [Proc. Am. Math. Soc. 102, No. 1, 37--42 (1988; Zbl 0656.20049); Mich. Math. J. 58, No. 1, 213--230 (2009; Zbl 1241.20004)].
Classification : 20G15, 20G40, 14L35, 20C08, 20G05
Keywords: refined Bruhat cells, Gelfand-Graev representations, closure patterns 
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     title = {On refinements of the {Bruhat} decomposition},
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Simion, Iulian I. On refinements of the Bruhat decomposition. Journal of Algebraic Combinatorics, Tome 43 (2016) no. 1, pp. 75-100. http://geodesic.mathdoc.fr/item/JAC_2016__43_1_a7/