Abstract: Infinite dimensional representations of a reductive Lie group can be studied by the algebraic geometry of flag varieties and the nilpotent cone. A relevant open problem is to describe the singular locus of K-orbit closures in the flag variety, but it is easier to compute approximations of the singular locus. We will see how resolutions of singularities enables us to compute certain approximations, and then describe some consequences in the corresponding representation theory.
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