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Braid group action on the category of matrix factorizations

Sergey Arkhipov
Onsdag, 29 januar, 2014, at 15:00-16:00, in Aud. D3 (1531-215)
Given an algebraic variety X with a distinguished function w called a potential we define the derived category of matrix factorizations DMF(X,w). For a variety X acted by an algebraic group K, with an invariant potential, we define the category DMF(X/K,w) of equivariant matrix factorizations due to Polishchuk and Vaintrob.

Our main example comes from Hamiltonian reduction. Let X be a K-variety. The moment map defines a potential on T^*X x Lie(K). For a free K-action we show that the corresponding equivariant derived category of matrix factorizations is equivalent to the category of coherent sheaves on the cotangent bundle to X/K.

We show that for a simple algebraic group G with the Borel subgroup B, we construct an action of the braid group of the corresponding type on the derived category of B-equivariant matrix factorizations on T^*X x Lie(B).
Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen