Quantum loop modules and quantum spin chains

DOI10.1142/S0217751X94001588zbMATH Open0988.81511arXivhep-th/9305135MaRDI QIDQ2775230

Daniel Altschüler, Brian Davies

Publication date: 26 February 2002

Published in: International Journal of Modern Physics A (Search for Journal in Brave)

Abstract: We construct level-0 modules of the quantum affine algebra $Uq$, as the $q$-deformed version of the Lie algebra loop module construction. We give necessary and sufficient conditions for the modules to be irreducible. We construct the crystal base for some of these modules and find significant differences from the case of highest weight modules. We also consider the role of loop modules in the recent scheme for diagonalising certain quantum spin chains using their $Uq$ symmetry.

Full work available at URL: https://arxiv.org/abs/hep-th/9305135

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Exactly solvable models; Bethe ansatz (82B23)

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Integrable representations of the quantum affine special linear superalgebra

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