Polynomial KP and BKP \(\tau\)-functions and correlators

DOI10.1007/s00023-021-01046-zzbMath1481.37074arXiv2011.13339OpenAlexW3153296301MaRDI QIDQ2231938

J. Harnad, Alexander Yu. Orlov

Publication date: 30 September 2021

Published in: Annales Henri Poincaré (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2011.13339

zbMATH Keywords

Schur functions\(\tau\)-functionsKP hierarchiesWick's theoremNimmo's Pfaffian ratio formula

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Exactly and quasi-solvable systems arising in quantum theory (81U15) 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) Special quantum systems, such as solvable systems (81Q80)

Related Items (9)

Tau functions, infinite Grassmannians, and lattice recurrences ⋮ Unitary matrix integrals, symmetric polynomials, and long-range random walks ⋮ The generalized Giambelli formula and polynomial KP and CKP tau-functions ⋮ BKP tau-functions as square roots of KP tau-functions ⋮ Extended Schur's \(Q\)-functions and the full Kostant-Toda hierarchy on the Lie algebra of type \(D\) ⋮ A new solvable two-matrix model and the BKP tau function ⋮ Linear transformations of vertex operators of Hall-Littlewood polynomials ⋮ Notes about the KP/BKP correspondence ⋮ Fredholm Pfaffian \(\tau \)-functions for orthogonal isospectral and isomonodromic systems

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