Orbital integrals in finite and infinite dimensions (Anton Alekseev, UniGE)

18.02.2020 16:00 – 17:00

Integrals of exponential functions over coadjoint orbits of compact Lie groups admit exact fixed point formulas. This discovery is due to Duistermaat-Heckman and Itzykson-Zuber. It would be interesting to generalise this fact to the infinite dimensional case.

In this talk, we will give a brief review of several constructions of infinite dimensional orbital integrals including the Frenkel integral over coadjoint orbits of central extensions of loop groups and the Stanford-Witten integral over coadjoint orbits of the Virasoro algebra. We will then suggest a new approach to infinite dimensional orbital integrals based on the quasi-classical asymptotic of characters of infinite dimensional Lie algebras.

The talk is based on a joint work with S. Shatashvili.

Lieu

Bâtiment: Battelle

Séminaire "Groupes de Lie et espaces des modules"

entrée libre