Multivariate hypergeometric functions as \(\tau\)-functions of Toda lattice and Kadomtsev-Petviashvili equation

DOI10.1016/S0167-2789(01)00158-0zbMath0988.37091arXivmath-ph/0003011OpenAlexW2055922956MaRDI QIDQ5940197

Alexander Yu. Orlov, D. M. Scherbin

Publication date: 22 July 2002

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0003011

zbMATH Keywords

hypergeometric functionsSchur polynomialToda lattice\(\tau\)-functionsKP hierarchies

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Discrete version of topics in analysis (39A12) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Connections of basic hypergeometric functions with quantum groups, Chevalley groups, (p)-adic groups, Hecke algebras, and related topics (33D80)

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Chern-Simons perturbative series revisited, 2D Toda τ functions, weighted Hurwitz numbers and the Cayley graph: Determinant representation and recursion formula, Combinatorial solutions to integrable hierarchies, Explicit closed algebraic formulas for Orlov-Scherbin \(n\)-point functions, A new symmetry of the colored Alexander polynomial, Toda hierarchies and their applications, Combinatorics of Bousquet-Mélou-Schaeffer numbers in the light of topological recursion, Polynomial KP and BKP \(\tau\)-functions and correlators, Fermionic construction of tau functions and random processes, Bilinear expansions of lattices of KP τ -functions in BKP τ -functions: A fermionic approach, 2D Yang–Mills Theory and Tau Functions, \(q\)-difference Kac-Schwarz operators in topological string theory, Soliton theory, symmetric functions and matrix integrals, Symmetries of the hypergeometric function \phantom{}_{𝑚}𝐹_{𝑚-1}, Constellations and \(\tau\)-functions for rationally weighted Hurwitz numbers

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