Inverting Hamiltonian Reduction - A Rep Theory Perspective

Abstract: Quantum Hamiltonian reduction is an algebraic procedure that produces new vertex algebras from known ones, with the best understood examples being the W-algebras that arise from affine vertex algebras. Recent work has focused on morally inverting this construction, which has important implications for representation theory. Moreover, since affine vertex algebras are intimately tied to their underlying Lie algebras, this inverse construction also provides new tools for constructing and studying weight modules over both finite and affine Lie algebras, which are of broader interest in algebra and mathematical physics. In this talk, I'll give an introduction to the ideas involved and illustrate the construction by showing how it naturally produces simple weight modules with infinite-dimensional weight spaces everywhere.

mathematical physicscommutative algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

Comments: Hybrid delivery (in person on University of Saskatchewan campus and via Zoom).

PIMS Geometry / Algebra / Physics (GAP) Seminar