Emmy-Noether-Seminar: Representation theory of the vertex algebra of chiral differential operators on a reductive group

Representation theory of the vertex algebra of chiral differential operators on a reductive group

Damien Simon (Paris)

Abstract: et G be a reductive algebraic group. There exists a Kac-Moody version of the usual algebra of differential operators on the group G called the vertex algebra of chiral differential operators on G. The study of the representation theory of this vertex algebra and its various quantum Hamiltonian reductions allow for a purely vertex algebraic formulation of the theory of D-modules on loop groups. In turn this allows one to translate some conjectures coming from the quantum geometric Langlands program.

For generic Kac-Moody levels, we will explain how to build simple objects in therelevant categories that match the expected combinatorics and formulate some conjectures that we check in the case of the multiplicative group.