“Quantisation of ‘semisimple’ coadjoint orbits, and relations with quantum de Rham spaces”
Lunedì 16 dicembre 2024, ore 14:30 - Aula 2AB45 - Gabriele Rembado (Marie Curie Global Université Montpellier)
Abstract
Let us work over the complex numbers: semisimple coadjoint orbits for reductive Lie groups have natural complex-algebraic symplectic structures, and their deformation quantisation involves Verma modules. Moreover, these orbits are local pieces of moduli spaces of regular singular meromorphic connections on Riemann surfaces, i.e. ‘tame’ de Rham spaces in nonabelian cohomology.
In this talk we will aim at a review of part of this story, and then explain how to deformation quantise ‘semisimple’ coadjoint orbits for (nonreductive) truncated current Lie groups. This involves generalisations of Verma modules, and is in turn intimately related with moduli spaces of irregular singular meromorphic connections -viz. the ‘wild’ de Rham spaces. If time allows we will also showcase the genus-zero examples, and sketch their 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.
