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Quantizations of Kleinian singularities

SPEAKER: Ivan Losev

TITLE: Quantizations of Kleinian singularities

ABSTRACT Kleinian singularities provide the simplest examples of singular Poisson varieties. There are several different ways to construct their quantizations: via taking the spherical subalgebras in some symplectic reflection algebras (Crawley-Bowey and Holland), via quantum Hamiltonian reduction (Holland) and via W-algebras. All these quantizations depend on some parameters from the same parameter space. We will outline the constructions of these quantizations. Then we will explain why the algebras obtained by the three constructions are isomorphic to each other and how the correspondence between the parameters looks like.