GTM Seminar

Speaker: Dmytro Matvieievskyi (Kavli IPMU)
Title: Root datum of a symplectic singularity, and applications to unitarity
Date (JST): Fri, May 31, 2024, 15:30 - 17:00
Place: Seminar Room A
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 natural reductive group G(X) corresponding to the geometry of 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, most importantly, show that it can be computed explicitly in 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. Time permitting, I explain why we believe that this bound should be very close to the actual unitary dual of G. This talk is based on a joint ongoing project with Ivan Losev and Lucas Mason-Brown.