The representation theory of quantised Lusztig slices

Abstract:

A common theme in modern representation theory is to study the representations of quantisations of symplectic varieties.  Lie theory can be formulated in this language using the Springer resolution.  In this talk I will describe this general idea, and then focus on a new family of algebras which quantise varieties arising from the geometric Satake correspondence.  I will give results and conjectures concerning the representation theory of these algebras relating them to semisimple Lie algebras.