# Centre for Quantum Geometry of Moduli Spaces # Seminar by Sergey Arkhipov (AU)

Title: Braid group action on the category of matrix factorizations

2014.01.27 | Jane Jamshidi

 Date Wed 29 Jan Time 15:00 — 16:00 Location Aud. D3

Abstract: 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).

Seminar
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