Affiliation:
1. Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA
Abstract
Abstract
The notion of a Harish-Chandra bimodule, that is, finitely generated $U(\mathfrak {g})$-bimodule with locally finite adjoint action, was generalized to any filtered algebra in a work of Losev [9]. Similarly to the classical case we can define the notion of a unitarizable bimodule. We investigate a question when the regular bimodule, that is, the algebra itself, for a deformation of Kleinian singularity of type $A$ is unitarizable. We obtain a partial classification of unitarizable regular bimodules.
Publisher
Oxford University Press (OUP)
Reference11 articles.
1. Irreducible unitary representations of the Lorentz group;Bargmann;Ann. of Math. (2),1947
2. Deformation quantization and superconformal symmetry in three dimensions;Beem;Comm. Math. Phys.,2017
3. Twisted traces and positive forms on quantized Kleinian singularities of type A;Etingof;SIGMA,2021
4. Unitary representations of rational Cherednik algebras;Etingof;Represent. Theory,2009