Unitary representations of \(U_{q} (\mathfrak s\mathfrak l(2,\mathbb R))\), the modular double and the multiparticle \(q\)-deformed Toda chain
From MaRDI portal
Publication:1348989
DOI10.1007/s002200100592zbMath1001.37067arXivhep-th/0102180OpenAlexW3123698889MaRDI QIDQ1348989
Publication date: 21 May 2002
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/hep-th/0102180
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Applications of Lie algebras and superalgebras to integrable systems (17B80) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)
Related Items
Check-operators and quantum spectral curves, \(q\)-Virasoro modular double and 3d partition functions, From rarefied elliptic beta integral to parafermionic star-triangle relation, Short proofs of the elliptic beta integrals, On Baxter \({\mathcal Q}\)-operators and their arithmetic implications, On three dimensional quiver gauge theories and integrability, Exact quantization conditions for the elliptic Ruijsenaars-Schneider model, Spectral extension of the quantum group cotangent bundle, Ds-ads structures in noncommutative Minkowski spaces, Quantization scheme for modular \(q\)-difference equations, Exact quantization conditions for the relativistic Toda lattice, THE CLASSICAL LIMIT OF REPRESENTATION THEORY OF THE QUANTUM PLANE, Defects and quantum Seiberg-Witten geometry, Baxter Operator and Baxter Equation for q-Toda and Toda2 Chains, Orthogonal Polynomials in Mathematical Physics, Gauge theories as matrix models, Representation of the quantum plane, its quantum double, and harmonic analysis on \(GL_q^+(2,\mathbb{R })\), Three-dimensional extensions of the Alday-Gaiotto-Tachikawa relation, A path model for Whittaker vectors, Spectrum and orthogonality of the Bethe ansatz for the periodic \(q\)-difference Toda chain on \(\mathbb{Z}_{m+1}\), Quantum exponentials for the modular double and applications in gravity models, Supergroup structure of Jackiw-Teitelboim supergravity, AGT on the S-duality wall, Finite-dimensional representations of the elliptic modular double, Refined 3d-3d correspondence, General modular quantum dilogarithm and beta integrals, The star-triangle relation, lens partition function, and hypergeometric sum/integrals, On \(q\)-deformed \({\mathfrak{gl}_{\ell+1}}\)-Whittaker function. I, On \(q\)-deformed \({\mathfrak{gl}_{\ell+1}}\)-Whittaker function. II, On Bailey pairs for \(\mathcal{N} = 2\) supersymmetric gauge theories on \(S_b^3/\mathbb{Z}_r\), \( \mathcal{S}\)-modular transformation of the \(\mathcal{N}=2\) superconformal algebra characters, 5D SYM on 3D deformed spheres, The gravity dual of supersymmetric gauge theories on a squashed three-sphere, Boundary operators in the \(O(n)\) and RSOS matrix models, A parafermionic hypergeometric function and supersymmetric \(6j\)-symbols, Exact relativistic Toda chain eigenfunctions from separation of variables and gauge theory, On the continuous series for \(\widehat{sl(2,\mathbb R)}\), The Schwarzian theory -- a Wilson line perspective, Calculating the partition function of \( \mathcal{N} = 2 \) gauge theories on \(S^{3}\) and AdS/CFT correspondence, SUSY gauge theories on squashed three-spheres, The endless beta integrals, \( {\text{SL}}\left( {2,\mathbb{R}} \right) \) Chern-Simons, Liouville, and gauge theory on duality walls, Elliptic hypergeometric function and $6j$-symbols for the SL(2,$\mathbb{C}$) group, Notes on SUSY gauge theories on three-sphere, Faddeev-Volkov solution of the Yang-Baxter equation and discrete conformal symmetry, Scattering of long folded strings and mixed correlators in the two-matrix model, BPS relations from spectral problems and blowup equations, On the separation of variables for the modular XXZ magnet and the lattice sinh-Gordon models, The pentagon relation and incidence geometry, The modular properties and the integral representations of the multiple elliptic gamma functions, On \(q\)-deformed \(\mathfrak{gl}_{\ell+1}\)-Whittaker function. III, Separation of variables for the quantum \(\mathrm{SL} (3, \mathbb{C} )\) spin magnet: eigenfunctions of the Sklyanin \(B\)-operator, Theta hypergeometric integrals, Ruijsenaars' hypergeometric function and the modular double of \(\mathcal {U}_{q}(\mathfrak {sl}_{2}(\mathbb C))\), Liouville quantum gravity --- holography, JT and matrices, Higher-level Appell functions, modular transformations, and characters, Generalized volume conjecture and the \(A\)-polynomials: The Neumann-Zagier potential function as a classical limit of the partition function, Dimer models and integrable systems, S-duality as a \(\beta\)-deformed Fourier transform, Supertetrahedra and superalgebras, \(S\)\^{}\{3\}/Z\_{}\{\(n\)\} partition function and dualities, Discrete series of representations for the modular double of the quantum group \(U_q (sl(2, \mathbb R))\), A LECTURE ON THE LIOUVILLE VERTEX OPERATORS (REVIEW), Continuous biorthogonality of an elliptic hypergeometric function, Wavefunctions, integrability, and open strings, Quantized mirror curves and resummed WKB, Riemann-Hilbert problems for the resolved conifold and non-perturbative partition functions, Solvable discrete quantum mechanics: q-orthogonal polynomials with q=1 and quantum dilogarithm, Mirror channel eigenvectors of the \(d\)-dimensional fishnets, Fine structure of Jackiw-Teitelboim quantum gravity, Supersymmetric vortex loops in 3D gauge theories, Topological phase, spin Chern-Simons theory and level rank duality on lens space, Hofstadter’s butterfly in quantum geometry, From quantum groups to Liouville and dilaton quantum gravity, Noncommutative hypergeometry, Unit circle elliptic beta integrals, Kernel functions and Bäcklund transformations for relativistic Calogero-Moser and Toda systems