Quantum superalgebras at roots of unity and non-Abelian symmetries of integrable models

Korff, C. and Roditi, I. (2002) Quantum superalgebras at roots of unity and non-Abelian symmetries of integrable models. Journal of Physics A: Mathematical and General, 35(24), pp. 5115-5137. (doi: 10.1088/0305-4470/35/24/310)

Abstract

We consider integrable vertex models whose Boltzmann weights (R-matrices) are trigonometric solutions to the graded Yang–Baxter equation. As is well known, the latter can be generically constructed from quantum affine superalgebras Uq(ĝ). These algebras do not form a symmetry algebra of the model for generic values of the deformation parameter q when periodic boundary conditions are imposed. If q is evaluated at a root of unity we demonstrate that in certain commensurate sectors one can construct non-Abelian subalgebras which are translation invariant and commute with the transfer matrix and therefore with all charges of the model. In the line of argument, we introduce the restricted quantum superalgebra U^resq(ĝ) and investigate its root of unity limit. We prove several new formulae involving supercommutators of arbitrary powers of the Chevalley–Serre generators and derive higher order quantum Serre relations as well as an analogue of Lustzig's quantum Frobenius theorem for superalgebras.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Korff, Professor Christian
• Authors: Korff, C., and Roditi, I.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Physics A: Mathematical and General
• Publisher: Institute of Physics Publishing Ltd.
• ISSN: 0305-4470