Root datum of a symplectic singularity, and applications to unitarity

：Dmytro Matvieievskyi（日本科维理宇宙物理学与数学研究所）
：2024-05-09 09:00
：海韵园实验楼105报告厅

报告人：Dmytro Matvieievskyi（日本科维理宇宙物理学与数学研究所）

时  间：2024年5月9日9:00

地  点：海韵园实验楼105报告厅

内容摘要:

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. 

个人简介：

Dr. Dmytro Matvieievskyi is a Project Researcher (postdoc) at Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU). He finished his Ph.D. degree in mathematics at Northeastern University in Summer 2022. His work belongs to the field of geometric representation theory. He is interested in symplectic singularities, orbit method, and finite W-algebras in particular.

 

联系人：余世霖