 
Summary: Transformation Groups, Vol. ?, No. ?, ??, pp. 1?? c
#Birkh˜auser Boston (??)
A DEODHARTYPE STRATIFICATION
ON THE DOUBLE FLAG VARIETY
BEN WEBSTER #
Department of Mathematics
University of California
Berkeley, CA 94720
MILEN YAKIMOV ##
Department of Mathematics
University of California
Santa Barbara, CA 93106
Abstract. We describe a partition of the double flag variety G/B +
× G/B  of a complex
semisimple algebraic group G analogous to the Deodhar partition on the flag variety G/B + .
This partition is a refinement of the stratification into orbits both for B +
× B  and for the
diagonal action of G, just as Deodhar's partition 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
