Algebraic Geometry Seminar

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Representations of Generalized Braid Groups on the Derived Category of a Git Quotient

Speaker: Daniel Halpern-Leistner, Columbia University

Location: Warren Weaver Hall 201

Date: Tuesday, February 9, 2016, 3:30 p.m.

Synopsis:

One consequence of the homological mirror symmetry conjecture predicts that many varieties will have "hidden symmetries" in the form of autoequivalences of their derived categories of coherent sheaves which do not correspond to any automorphism of the underlying variety. In fact there is a certain "complexified Kähler moduli space" whose fundamental group conjecturally acts on the derived category. When the space in question is the cotangent bundle of a flag variety, actions of this kind have been studied intensely in the context of geometric representation theory and Kazhdan-Lusztig theory. We establish the conjectured group action on the derived category of any variety which arises as a symplectic or hyperkähler reduction of a (certain kind of) linear representation of a compact Lie group. Our methods are quite explicit and essentially combinatorial.