Quantized Knizhnik-Zamolodchikov equations, quantum Yang-Baxter equation, and difference equations for \(q\)-hypergeometric functions

DOI10.1007/BF02101745zbMath0807.17014OpenAlexW2094416057MaRDI QIDQ1328224

Alexander Varchenko

Publication date: 5 March 1995

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

Full work available at URL: https://doi.org/10.1007/bf02101745

zbMATH Keywords

difference equations\(q\)-hypergeometric functions\(q\)-Knizhnik-Zamolodchikov equationsquantum Knizhnik- Zamolodchikov equation

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) PDEs in connection with quantum mechanics (35Q40)

Related Items

Connection formula of symmetric \(A\)-type Jackson integrals, Geometric \(q\)-hypergeometric functions as a bridge between Yangians and quantum affine algebras, Quantum \({\mathcal W}\)-algebras and elliptic algebras, Unnamed Item, \(q\)-difference systems for the Jackson integral of symmetric Selberg type, Elliptic and \(K\)-theoretic stable envelopes and Newton polytopes, Askey-Wilson polynomials by means of a \(q\)-Selberg type integral, Noncommutative Hypergeometric and Basic Hypergeometric Equations, Quantum $q$-Langlands Correspondence, MONODROMY OF SOLUTIONS OF THE ELLIPTIC QUANTUM KNIZHNIK–ZAMOLODCHIKOV–BERNARD DIFFERENCE EQUATIONS, Three-dimensional mirror self-symmetry of the cotangent bundle of the full flag variety, Form factors of the \(XXZ\) Heisenberg spin-\(\frac 12\) finite chain, Correlation functions of the \(XXZ\) Heisenberg spin-\({1\over 2}\) chain in a magnetic field, Derivation of q-difference equation from connection matrix for selberg type jackson integrals, Partial flag varieties, stable envelopes, and weight functions, Gauss decomposition of connection matrices and application to Yang-Baxter equation. I, Gauss decomposition of connection matrices and application to Yang-Baxter equation. II

Cites Work

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• Topological representations of the quantum group \(U_ q(sl_ 2)\)
• Monodromy representations of braid groups and Yang-Baxter equations
• Current algebras and Wess-Zumino model in two dimensions
• Finiteness of a cohomology associated with certain Jackson integrals
• Arrangements of hyperplanes and Lie algebra homology
• Quantum affine algebras and holonomic difference equations
• Jackson-type integrals, Bethe vectors, and solutions to a difference analog of the Knizhnik-Zamolodchikov system
• Cohomology of local systems on the complement of hyperplanes
• Connection problem in holonomicq-difference system associated with a Jackson integral of Jordan-Pochhammer type