Graham's Variety and Perverse Sheaves on the Nilpotent Cone

Details Graham's Variety and Perverse Sheaves on the Nilpotent Cone Graham's Variety and Perverse Sheaves on the Nilpotent Cone

2011-11-09

arxiv.org/abs/1111.2343v1

Mathematics

Representation Theory

Scientific paper

In recent work, Graham has constructed a variety with a map to the nilpotent cone which is similar in some ways to the Springer resolution. One aspect in which Graham's map differs is that it is not in general an isomorphism over the principal orbit, but rather the universal covering map. This map gives rise to a certain semisimple perverse sheaf on the nilpotent cone, and we discuss here the problem of describing the summands of this perverse sheaf. For type $A_n$, a key tool is Tymoczko's description of an affine paving of Springer fibers.

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