\(\mathrm{SL}(2,\mathbb{C})\) Gustafson integrals

DOI10.3842/SIGMA.2018.030zbMath1387.81237arXiv1711.07822OpenAlexW2768859652MaRDI QIDQ1747890

Pavel A. Valinevich, Alexander N. Manashov, Sergey E. Derkachov

Publication date: 27 April 2018

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1711.07822

zbMATH Keywords

separation of variablesBaxter operators

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) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Other hypergeometric functions and integrals in several variables (33C70) Inverse scattering problems in quantum theory (81U40) Groups and algebras in quantum theory and relations with integrable systems (81R12) Applications of Lie algebras and superalgebras to integrable systems (17B80) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Yang-Baxter equations (16T25)

Related Items

An analog of the Dougall formula and of the de Branges-Wilson integral, The Gelfand–Tsetlin basis for infinite-dimensional representations of gln(C), Mellin-Barnes transformation for two-loop master-diagram, On Gustafson integrals for the group \(\mathrm{SL}(2,\mathbb{R} )\), Barnes-Ismagilov integrals and hypergeometric functions of the complex field, The endless beta integrals, On complex gamma-function integrals

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Elliptic hypergeometry of supersymmetric dualities
• Exact solution of the Faddeev-Volkov model
• Inversions of integral operators and elliptic beta integrals on root systems
• Quantum inverse problem method. I
• Yang-Baxter equation and representation theory. I
• A master solution of the quantum Yang-Baxter equation and classical discrete integrable equations
• Quantum mechanics of null polygonal Wilson loops
• Tensor product spaces
• Iterative construction of eigenfunctions of the monodromy matrix for $SL(2,\mathbb {C})$ magnet
• Elliptic beta integrals and solvable models of statistical mechanics
• New solutions of the star–triangle relation with discrete and continuous spin variables
• The importance of the Selberg integral
• Some Hypergeometric Orthogonal Polynomials
• Some q-Beta and Mellin–Barnes Integrals with Many Parameters Associated to the Classical Groups
• Some q-Beta and Mellin-Barnes Integrals on Compact Lie Groups and Lie Algebras
• Some q-Beta Integrals on $SU(n)$ and $Sp(n)$ That Generalize the Askey–Wilson and Nasrallah–Rahman Integrals
• Theta hypergeometric integrals
• Hypergeometric functions over an arbitrary field
• Boundary conditions for integrable quantum systems
• Comment on star–star relations in statistical mechanics and elliptic gamma-function identities
• On $BC$ type basic hypergeometric orthogonal polynomials
• Spin chains and Gustafson’s integrals
• Gustafson integrals for $SL(2, \mathbb{C})$ spin magnet
• A new solution of the star–triangle relation
• Noncompact Heisenberg spin magnets from high-energy QCD. I: Baxter Q-operator and separation of variables