Talks

Three dimensional gravity in Fefferman-Graham or BMS gauge is entirely described by the coadjoint representation of its asymptotic asymptotic symmetry group. A group-theoretical attempt at quantization requires one to quantize not only individual but the whole collection of coadjoint orbits. This is where model spaces come in. We propose a definition of a model space for generic Lie groups in terms of constrained Hamiltonian systems and begin by studying its quantization in the simplest case of SU(2).

 

Based on work in preparation done in collaboration with Thomas Smoes

The chiralization in the title denotes a certain procedure which turns cluster X-varieties into q-W algebras. Many important notions from cluster and q-W worlds, such as mutations, global functions, screening operators, R-matrices, etc emerge naturally in this context. In particular, we discover new bosonizations of q-W algebras and establish connections between previously known bosonizations. If time permits, I will discuss potential applications of our approach to the study of 3d topological theories and local systems with affine gauge groups.

 

Based on a joint project with J. Shiraishi, J.E. Bourgine, B. Feigin, A. Shapiro, and G. Schrader.