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A DEODHAR TYPE STRATIFICATION ON THE DOUBLE FLAG VARIETY
 

Summary: A DEODHAR TYPE STRATIFICATION
ON THE DOUBLE FLAG VARIETY
BEN WEBSTER AND MILEN YAKIMOV
Abstract. We describe a stratification on the double flag variety G/B +
×
G/B - of a complex semisimple algebraic group G analogous to the Deodhar
stratification on the flag variety G/B + , which is a refinement of the stratifi­
cation into orbits both for B +
×B - and for the diagonal action of G, just as
Deodhar's stratification refines the orbits of B + and B - .
We give a coordinate system on each stratum, and show that all strata are
coisotropic subvarieties. Also, we discuss possible connections to the positive
and cluster geometry of G/B +
× G/B - , which would generalize results of
Fomin and Zelevinsky on double Bruhat cells and Marsh and Rietsch on double
Schubert cells.
1. Introduction
Let G be a complex semisimple algebraic group with a fixed pair of dual Borel
subgroups B ± and let T = B +
# B - be the corresponding maximal torus of G.

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics