Posted in

Speaker:

Alexander Goncharov
Affiliation:

Yale University/MPIM
Date:

Thu, 11/05/2023 - 15:00 - 16:00
Location:

MPIM Lecture Hall
Parent event:

MPI-Oberseminar Let S be an oriented surface with a finite collection of points on the boundary, and G any split reductive group (with connected center).

Then there is a moduli space P(G,S) parametrizing G-local systems on S equipped with certain boundary data.

It carries a canonical cluster Poisson structure, equivariant under the action of a large discrete group, containing the mapping class group of S.

Therefore the cluster quantization construction, developed by V. Fock and myself, assigns to the pair (G,S) a non-commutative *-algebra A(G,S;h)

together with its principal series of (infinite dimensional) *-representations. The assignment S --> *-representations of A(G,S;h)

should provide a continuous version of the modular functor.

The representation theory of quantum groups becomes a part of the representation theory of these algebras.

Its new feature is that both objects and Hom's between them are representations of the algebras A(G,S;h).

The talk is based on the joint work with Linhui Shen.

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