Quantum orbits and wild de Rham spaces

Abstract

Coadjoint orbits of complex reductive Lie groups have natural symplectic structures, which can be quantized using Verma modules. Moreover, such orbits are local pieces of moduli spaces of regular singular connections on Riemann surfaces---viz. `tame' de Rham spaces in nonabelian Hodge theory. In this talk we will aim at a review of part of this story, and then explain how to quantize `semisimple' coadjoint orbits of (nonreductive) truncated current Lie groups. This involves generalisations of Verma modules, and is in turn intimately related with moduli spaces of irregular singular connections---viz. `wild' de Rham spaces. If time allows, we will showcase examples on the sphere and sketch the relation with conformal field theory. [This is past work with D. Calaque, G. Felder, and R. Wentworth; as well as work in progress with M. Chaffe and L. Topley].

Lo speaker si presenta al Dipartimento in qualità di candidato al bando “Rita Levi Montalcini”.