A solution to quantum Knizhnik-Zamolodchikov equations and its application to eigenvalue problems of the Macdonald type

DOI10.1215/S0012-7094-96-08524-5zbMath0889.17009OpenAlexW1565542143MaRDI QIDQ674640

Katsuhisa Mimachi

Publication date: 28 January 1998

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-96-08524-5

zbMATH Keywords

quantum Knizhnik-Zamolodchikov equation\(q\)-Selberg integralMacdonald type eigenvalue problem

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) PDEs in connection with quantum mechanics (35Q40) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

Related Items (12)

An integral representation of eigenfunctions for Macdonald's \(q\)-difference operators ⋮ QKZ-Ruijsenaars correspondence revisited ⋮ Unnamed Item ⋮ Integral representations of the Wilson polynomials and the continuous dual Hahn polynomials ⋮ Askey-Wilson polynomials by means of a \(q\)-Selberg type integral ⋮ A reproducing kernel for nonsymmetric Macdonald polynomials ⋮ Affine Hecke algebras and raising operators for Macdonald polynomials ⋮ The exact finite size ground state of the O(n= 1) loop model with open boundaries ⋮ Eigenfunctions of MacDonald's \(q\)-difference operator for the root system of type \(C_n\) ⋮ Determinant formula for solutions of the quantum Knizhnik-Zamolodchikov equation associated with \(U_q (sl_n)\) at \(|q|=1\) ⋮ A multidimensional generalization of the Barnes integral and the continuous Hahn polynomial ⋮ A duality of MacDonald-Koornwinder polynomials and its application to integral representations

Cites Work

• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• Quantum affine algebras and holonomic difference equations
• Quantum Knizhnik-Zamolodchikov equations and affine root systems
• Connection formula of symmetric \(A\)-type Jackson integrals
• \(R\)-matrix arising from affine Hecke algebras and its application to Macdonald's difference operators
• Induced representations of double affine Hecke algebras and applications
• Singular vectors of the Virasoro algebra in terms of Jack symmetric polynomials
• Integral representations of the Macdonald symmetric polynomials
• Affine Hecke Algebras and Their Graded Version
• Connection problem in holonomicq-difference system associated with a Jackson integral of Jordan-Pochhammer type
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