Orthogonality and the qKZB-heat equation for traces of \(U_q({\mathfrak g})\)-intertwiners

DOI10.1215/S0012-7094-04-12814-3zbMath1160.17305arXivmath/0302071OpenAlexW2070315316MaRDI QIDQ2572631

Alexander Varchenko, Pavel I. Etingof

Publication date: 4 November 2005

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

Full work available at URL: https://arxiv.org/abs/math/0302071

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) Basic hypergeometric functions associated with root systems (33D67) Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) (32G34) Hypergeometric functions associated with root systems (33C67)

Related Items

Degenerate integrability of quantum spin Calogero-Moser systems, Traces of intertwiners for quantum affine \(\mathfrak{sl}_2\) and Felder-Varchenko functions, Orthogonality relations and Cherednik identities for multivariable Baker-Akhiezer functions, Baker-Akhiezer functions and generalised Macdonald-Mehta integrals, \((q, t)\)-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On Macdonald's \(\eta\)-function formula, the Laplacian and generalized exponents
• Traces of intertwiners for quantum groups and difference equations. I
• Macdonald polynomials and algebraic integrability
• Dynamical Weyl groups and applications
• Exchange dynamical quantum groups
• How to regularize singular vectors and kill the dynamical Weyl group
• \(q\)-deformed KZB heat equation: completeness, modular properties and \(\text{SL}(3,\mathbb Z)\).
• Traces of intertwiners for quantum groups and difference equations
• Macdonald's polynomials and representations of quantum groups
• Macdonald's evaluation conjectures and difference Fourier transform
• MONODROMY OF SOLUTIONS OF THE ELLIPTIC QUANTUM KNIZHNIK–ZAMOLODCHIKOV–BERNARD DIFFERENCE EQUATIONS
• On Cherednik-Macdonald-Mehta identities
• The elliptic gamma function and \(\text{SL}(3,\mathbb Z)\ltimes\mathbb Z^3\).
• The \(q\)-deformed Knizhnik-Zamolodchikov-Bernard heat equation.