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Representation theory of very non-standard quantum so(2N-1)

Lookup NU author(s): Dr Stefan Kolb, Dr Jake Stephens

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Abstract

We classify the finite dimensional representations of the quantum symmetric pair coideal subalgebra B_c of type DII corresponding to the symmetric pair (so(2N), so(2N − 1)). For B_c defined over an arbitrary field k and q ∈ k \ {0} not a root of unity we establish a one-to-one correspondence between finite dimensional, simple B_c-modules and dominant integral weights for so(2N − 1). We use specialisation to show that the category of finite dimensional B_c -modules is semisimple if char(k) = 0 and q is transcendental over Q. In this case the characters of simple B_c-modules are given by Weyl’s character formula. This means in particular that the quantum symmetric pair of type DII can be used to obtain Gelfand-Tsetlin bases for irreducible representations of the Drinfeld-Jimbo quantum group U_q(so(2N)).

Publication metadata

Author(s): Kolb S, Stephens J

Publication type: Article

Publication status: Published

Journal: Journal of Pure and Applied Algebra

Year: 2025

Volume: 229

Issue: 7

Print publication date: 01/07/2025

Online publication date: 08/05/2025

Acceptance date: 30/04/2025

Date deposited: 15/05/2025

Publisher: Elsevier BV

URL: https://doi.org/10.1016/j.jpaa.2025.107990

DOI: 10.1016/j.jpaa.2025.107990

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