Representations of affine Lie algebras, elliptic \(r\)-matrix systems, and special functions

DOI10.1007/BF02099981zbMath0803.17008arXivhep-th/9303018MaRDI QIDQ1317403

Pavel I. Etingof

Publication date: 9 January 1995

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

Full work available at URL: https://arxiv.org/abs/hep-th/9303018

zbMATH Keywords

intertwining operatorsclassical Yang-Baxter equationaffine Lie algebramonodromy representationsKnizhnik- Zamolodchikov equationsmodular invariant equation

Mathematics Subject Classification ID

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67) Two-dimensional field theories, conformal field theories, etc. in quantum mechanics (81T40) PDEs in connection with quantum mechanics (35Q40)

Related Items (8)

Planck constant as spectral parameter in integrable systems and KZB equations ⋮ Representations of affine Lie algebras, parabolic differential equations, and Lamé functions ⋮ Traces of intertwiners for quantum affine algebras and difference equations (after Etingof-Schiffmann-Varchenko) ⋮ Elliptic KZ system, braid group of the torus and Vassiliev invariants ⋮ Schlesinger transformations for elliptic isomonodromic deformations ⋮ Folded and contracted solutions of coupled classical dynamical Yang-Baxter and reflection equations ⋮ From VOAs to short star products in SCFT ⋮ TRIGONOMETRIC DEGENERATION AND ORBIFOLD WESS-ZUMINO-WITTEN MODEL I

Cites Work

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• Monodromy representations of braid groups and Yang-Baxter equations
• Current algebras and Wess-Zumino model in two dimensions
• Discrete groups and the integrability of quantum systems
• Integral solutions of trigonometric Knizhnik-Zamolodchikov equations and Kac-Moody algebras
• Arrangements of hyperplanes and Lie algebra homology
• Quantum affine algebras and holonomic difference equations
• Solutions of the classical Yang-Baxter equation for simple Lie algebras

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