30. Apr 2026

Reduction by stages for affine W-algebras

Algebra, Geometry and Topology Seminar

Datum: 30. April 2026 | 13:15 – 15:00
Sprecher: Thibault Juillard, University of Hamburg
Veranstaltungsort: Office Bldg West / Ground floor / Heinzel Seminar Room (I21.EG.101)
Sprache: Englisch

Affine W-algebras form a family of vertex algebras parametrised by nilpotent orbits in simple Lie algebras. These are algebraic structures generalising infinite-dimensional Lie algebras such as affine Kac–Moody algebras or Virasoro algebras.
In this talk, I will present a joint work with Naoki Genra about "reduction by stages". Given two nilpotent orbits, in the same Lie algebra, satisfying some compatibility conditions, we prove that one of the corresponding W-algebras can be reconstructed as the quantum Hamiltonian reduction of the other one. Our approach is geometric, using the fact that each W-algebra is the quantisation of some Poisson variety, the Slodowy slice associated with the corresponding nilpotent orbit.
As an application, I will present a sufficient condition on a pair of nilpotent orbits in type A to get a natural embedding of affine W-algebras. This an analogue of the combinatorial rule established by Kraft and Procesi in their study of Slodowy slices in the 80's.