q-Deformed Orthogonal and Pseudo-Orthogonal Algebras and Their Representations

2002/03/19 by A. M. Gavrilik, A. U. Klimyk · 2 citations
Mathematics · Physics and Astronomy · #math.QA #gr-qc #hep-th #math-ph #math.MP #math.RT

paper · pdf · doi:10.1007/bf00420371

published as Lett.Math.Phys. 21 (1991) 215-220 · Latex, 5 pages; an old paper (1991) posted for archival purposes

arxiv created 2002/03/19 · arxiv updated 2015/06/26

Abstract

Deformed orthogonal and pseudo-orthogonal Lie algebras are constructed which differ from deformations of Lie algebras in terms of Cartan subalgebra and root vectors and which make it possible to construct representations by operators acting according to Gel'fand--Tsetlin-type formulas. Unitary representations of the q-deformed algebras U_q(so_n,1) are found.

Cited by

• The quantum spin Brauer category
• Boundary q-characters of evaluation modules for split quantum affine symmetric pairs