Quantum affine Lie algebras, Casimir invariants, and diagonalization of the braid generator

DOI10.1063/1.530641zbMath0833.17009arXivhep-th/9311041OpenAlexW3100718290WikidataQ60732533 ScholiaQ60732533MaRDI QIDQ4837161

Yao-Zhong Zhang, Mark D. Gould

Publication date: 4 July 1995

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/hep-th/9311041

zbMATH Keywords

universal \(R\)-matrixcentral elementsCasimir invariantsbraid generatorintegrable irreducible highest weight representationeigenvalue formulasinfinite-dimensional quantum affine Lie algebrasquantum Clebsch-Gordan decomposition

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)

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Cites Work

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• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• Quantum deformations of certain simple modules over enveloping algebras
• Quantum groups and diagonalization of the braid generator
• The uniqueness theorem for the universal \(R\)-matrix
• Quantized affine Lie algebras and diagonalization of braid generators
• KAC-MOODY AND VIRASORO ALGEBRAS IN RELATION TO QUANTUM PHYSICS
• Generalized Gel’fand invariants and characteristic identities for quantum groups
• ON SEIFERT CIRCLES AND FUNCTORS FOR TANGLES
• Unitarity and complete reducibility of certain modules over quantized affine Lie algebras