An application of Aomoto-Gelfand hypergeometric functions to the SU(n) Knizhnik-Zamolodchikov equation

DOI10.1007/BF02102089zbMath0714.33012OpenAlexW1641543654MaRDI QIDQ750691

Atsushi Matsuo

Publication date: 1990

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02102089

zbMATH Keywords

Knizhnik-Zamolodchikov equationgeneralized hypergeometric differential equations

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Elliptic integrals as hypergeometric functions (33C75)

Related Items (19)

A note on generalized hypergeometric functions, KZ solutions, and gluon amplitudes ⋮ Gaudin model, Bethe ansatz and critical level ⋮ On the Veselov-Felder reconstruction formula in the theory of Calogero-Sutherland operators ⋮ Solutions of KZ differential equations modulo \(p\) ⋮ Integral and theta formulae for solutions of \(sl_N\) Knizhnik-Zamolodchikov equation at level zero ⋮ Fock space representations of affine Lie algebras and integral representations in the Wess-Zumino-Witten models ⋮ Integral solutions of trigonometric Knizhnik-Zamolodchikov equations and Kac-Moody algebras ⋮ Conformal blocks of minimal models on a Riemann surface ⋮ Arrangements of hyperplanes and Lie algebra homology ⋮ Jackson integrals of Jordan-Pochhammer type and quantum Knizhnik-Zamolodchikov equations ⋮ Integrable connections related to zonal spherical functions ⋮ The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz ⋮ The \(\mathbb{F}_p\)-Selberg integral of type \(A_n\) ⋮ Generalized hypergeometric functions on the torus and the adjoint representation of \(U_ q(sl_ 2)\) ⋮ On the solutions of Knizhnik-Zamolodchikov system ⋮ Conformal field theory and the exact solution of the BCS Hamiltonian ⋮ Bethe eigenvectors of higher transfer matrices ⋮ Quantum algebra structure of certain Jackson integrals ⋮ Hypergeometric solutions of trigonometric KZ equations satisfy dynamical difference equations

Cites Work

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• General hypergeometric functions on complex Grassmannians
• Representations of affine Kac-Moody algebras, bosonization and resolutions
• Fock space representations of the Virasoro algebra. Intertwining operators
• Gauss-Manin connection of integral of difference products
• Infinite conformal symmetry in two-dimensional quantum field theory
• Current algebras and Wess-Zumino model in two dimensions
• HYPERGEOMETRIC-TYPE INTEGRALS AND THE $\mathfrak{sl}(2, {\rm C})$ KNIZHNIK-ZAMOLODCHIKOV EQUATION

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