Work

Braided module categories via quantum symmetric pairs

Year: 2019

Type: article

Abstract: Let g be a finite-dimensional complex semisimple Lie algebra. The finite-dimensional representations of the quantized enveloping algebra U q ( g ) form a braided monoidal category O int . We show that the category of finite-dimensional representations of a quantum symmetric pair coideal subalgebra B c , s of U q ( g ) is a braided module category over an equivariantization O int ⟨ σ ⟩ of O int . The braiding for B c , s is realized by a universal K-matrix which lies in a completion of B c , s ⊗ U q ( g ) . We apply these results to describe a distinguished basis of the center of B c , s .

Source: Proceedings of the London Mathematical Society

DOI: 10.1112/plms.12303

Author: Stefan Kolb

Institution: Newcastle University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Universität Hamburg, Engineering and Physical Sciences Research Council

Awards: G1197343400, Coideals in representation theory and integrability