Cell decompositions of double Bott-Samelson varieties

2013/10/17 by Mouquin, Victor
#14M15 (Primary) #70G45 (Secondary) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1310.4642

Abstract

Let G be a connected complex semisimple Lie group. Webster and Yakimov have constructed partitions of the double flag variety G/B x G/B_, where (B, B_) is a pair of opposite Borel subgroups of G, generalizing the Deodhar decompositions of G/B. We show that these partitions can be better understood by constructing cell decompositions of a product of two Bott-Samelson varieties Z_{u, v}, where u and v are sequences of simple reflections. We construct coordinates on each cell of the decompositions and in the case of a positive subexpression, we relate these coordinates to regular functions on a particular open subset of Z_{u, v}. Our motivation for constructing cell decompositions of Z_u,v was to study a certain natural Poisson structure on Z_u,v.

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