Tensor product varieties, perverse sheaves and stability conditions

Details Tensor product varieties, perverse sheaves and stability conditions Tensor product varieties, perverse sheaves and stability conditions

2011-09-21

arxiv.org/abs/1109.4578v3

Mathematics

Representation Theory

Section 7 rewritten. Comments welcome

Scientific paper

We show that the space spanned by the class of simple perverse sheaves in [Zh08] without localization is isomorphic to the tensor product of a Verma module with a tensor product of irreducible integrable modules of the quantum enveloping algebra associated with a graph. Under the isomorphism, the simple perverse sheaves get identified with the canonical basis elements of the tensor product module. We also show that the two stability conditions coincide in the localization process in [Zh08], by using supports and singular supports of complexes of sheaves, respectively.

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