## arXiv Analytics

### arXiv:2003.11508 [math.RT]AbstractReferencesReviewsResources

#### On unitarizable Harish-Chandra bimodules for deformations of Kleinian singularities

Published 2020-03-25Version 1

The notion of a Harish-Chandra bimodule, i.e. finitely generated $U(\mathfrak{g})$-bimodule with locally finite adjoint action, was generalized to any filtered algebra in a work of Losev [Ivan Losev, Dimensions of irreducible modules over W-algebras and Goldie ranks. arXiv:1209.1083]. Similarly to the classical case we can define the notion of a unitarizable bimodule. We investigate a question when the regular bimodule, i.e. the algebra itself, for a deformation of Kleinian singularity of type $A$ is unitarizable. We obtain a partial classification of unitarizable regular bimodules.

On Irreducible weight representations of a new deformation $U_{q}(sl_{2})$ of $U(sl_{2})$