Noncommutative Hypergeometry

Abstract

A certain special function of the generalized hypergeometric variety is shown to fulfill a host of useful noncommutative identities.

14 pages, LaTeX (amsart)

References in corpus (2)

• Unitary representations of $U_{q}(\mathfrak{sl}(2,\RR))$, the modular double, and the multiparticle q-deformed Toda chains
• R-operator, co-product and Haar-measure for the modular double of U_q(sl(2,R))

Cited by in corpus (50)

• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• Elliptic hypergeometry of supersymmetric dualities
• Essays on the theory of elliptic hypergeometric functions
• Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
• R-operator, co-product and Haar-measure for the modular double of U_q(sl(2,R))
• Reconstruction of Baxter Q-operator from Sklyanin SOV for cyclic representations of integrable quantum models
• Classical and Quantum Dilogarithm Identities
• An analog of a modular functor from quantized Teichm"uller theory
• 3d N=2 mirror symmetry, pq-webs and monopole superpotentials
• Completeness of Bethe Ansatz by Sklyanin SOV for Cyclic Representations of Integrable Quantum Models
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• 3d dualities from 2d free field correlators: recombination and rank stabilization
• Quantum Riemann Surfaces in Chern-Simons Theory
• A new formulation of the Teichmüller TQFT
• Complex Quantum Chern-Simons
• Chern-Simons Theory and S-duality
• Baxter operators with deformed symmetry
• The universal Racah-Wigner symbol for Uq(osp(1|2))
• Elliptic hypergeometric functions
• Elliptic beta integrals and solvable models of statistical mechanics
• Discrete evolution for the zero-modes of the Quantum Liouville Model
• Baxter Q-operators of the XXZ chain and R-matrix factorization
• Self-dual Continuous Series of Representations for U_q(sl(2)) and U_q(osp(1|2))
• Quantum Teichmüller space from quantum plane
• From Principal Series to Finite-Dimensional Solutions of the Yang-Baxter Equation
• Baxter operator and Baxter equation for $q$-Toda and Toda${}_2$ chains
• 6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories
• Discrete Liouville equation and Teichmüller theory
• Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group
• On beta pentagon relations
• Quantization of the Zigzag Model
• The integrable structure of nonrational conformal field theory
• The R-operator for Modular Double
• On a Gopakumar-Vafa form of partition function of Chern-Simons theory on classical and exceptional lines
• On the spectral theory of one functional-difference operator from conformal field theory
• Summation formulae for noncommutative hypergeometric series
• Chiral Potts model and the discrete Sine-Gordon model at roots of unity
• Supersymmetry and the Modular Double
• On Bailey pairs for $\mathcal{N}=2$ supersymmetric gauge theories on $S_b^3/{\mathbb{Z}}_r$
• The Graphs of Quantum Dilogarithm
• Classical and Quantum Dynamics on Orbifolds
• On tensor product decomposition of positive representations of ${\mathcal{U}}_{q\tilde{q}}(\mathfrak{sl}(2,\mathbb{R}))$
• On modular double of semisimple quantum groups
• Discrete series of representations for the modular double of U_q(sl(2,R))
• Heisenberg double and Drinfeld double of the quantum superplane
• Finite dimensional quantum Teichmüller space from the quantum torus at root of unity
• On explicit realization of algebra of complex divided powers of $U_q(\mathfrak{sl}(2))$
• Baxterization of GL_q(2) and its application to the Liouville model and some other models on a lattice
• Zero modes for the quantum Liouville model