Emmy-Noether-Seminar: Virasoro type reductions and their inverses

Virasoro type reductions and their inverses

Justine Fasquel (Melbourne)

Abstract: W-algebras form a broad family of vertex algebras built from a simple Lie algebra and parametrised by its nilpotent orbits. They are constructed by applying quantum Hamiltonian reductions to affine vertex algebras, a sophisticated process that remains largely mysterious. Partial and inverse quantum hamiltonian reductions have been introduced to address the intricacies of general reductions. They rely respectively on splitting and inverting the reductions.

In this talk, we will focus on the first example of quantum Hamiltonian reduction — which results in constructing the famous Virasoro vertex algebra — and its inverse. We should also mention some applications to the representation theory. If time allows, we will then discuss generalisations of the Virasoro partial and inverse reductions to a substantial family of W-algebras associated with height-two nilpotent orbits. These results were obtained in collaboration with V. Kovalchuk and S. Nakatsuka.