Speaker：Dmytro Matvieievskyi (Kavli IPMU)

Time：2024-5-9, 9:00

Location：Conference Room 105 at Experiment Building at Haiyun Campus

Abstract:

A conical symplectic singularity X comes with a certain data parameterizing its deformations, namely a Namikawa-Cartan space P and a Namikawa-Weyl group W. A natural question is whether there is a reductive group G(X) corresponding to X such that P and W are the Cartan space and the Weyl group of G(X) respectively. In this talk I propose a construction of such a group and compute some examples. The main motivation and the main source of examples is when X is an affinization of a nilpotent orbit cover for some complex semisimple group G. Then quantizations of such X are deeply connected with the study of irreducible representations of G. We use the constructed group G(X) to give a conjectural bound on the unitary dual of G. This talk is based on a joint ongoing project with Ivan Losev and Lucas Mason-Brown.