MS Seminar (Mathematics - String Theory)

Speaker: Iordan Ganev (Institute of Science and Technology Austria)
Title: Quantum multiplicative quiver varieties at a root of unity
Date: Tue, Jun 18, 2019, 13:15 - 14:45
Place: Seminar Room A
Abstract: A common phenomenon when quantizing at roots of unity is the appearance of sheaves of Azumaya algebras on various moduli spaces. We focus on an instance of this phenomenon arising from the study of quiver representations. We begin by recalling the definition of multiplicative quiver varieties, which are constructed via Hamiltonian reduction along a group-valued moment map, and their quantizations. We state several results, and describe the techniques used in the proofs. Our methods are part of a general mechanism involving a version of quantum Hamiltonian reduction that relies on Lusztig's quantum Frobenius homomorphism and the notion of Poisson orders. This is joint work with D. Jordan and P. Safronov.