\(Q\)-operator and factorised separation chain for Jack polynomials

DOI10.1016/S0019-3577(03)90057-7zbMath1057.33011arXivmath/0306242WikidataQ59721869 ScholiaQ59721869MaRDI QIDQ1432906

Vadim B. Kuznetsov, Vladimir V. Mangazeev, Evgueni K. Sklyanin

Publication date: 22 June 2004

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0306242

zbMATH Keywords

hypergeometric integralssymmetric groupJack polynomialsSekiguchi operatorsBaxter's method

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Other hypergeometric functions and integrals in several variables (33C70)

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Quantum Bäcklund transformations: some ideas and examples ⋮ Baxter's Q-operators and operatorial Bäcklund flow for quantum (super)-spin chains ⋮ On the Yang-Baxter equation for the six-vertex model ⋮ Explicit solution of the (quantum) elliptic Calogero-Sutherland model ⋮ Noncompact \(\mathrm{sl}(N)\) spin chains: BGG-resolution, Q-operators and alternating sum representation for finite-dimensional transfer matrices ⋮ On combinatorial expansion of the conformal blocks arising from AGT conjecture ⋮ Baxter operators for arbitrary spin ⋮ Separation of variables for symplectic characters ⋮ A unified construction of generalized classical polynomials associated with operators of Calogero-Sutherland type ⋮ Source identity and kernel functions for elliptic Calogero-Sutherland type systems ⋮ Classical tau-function for quantum spin chains ⋮ Orthogonality of super‐Jack polynomials and a Hilbert space interpretation of deformed Calogero–Moser–Sutherland operators ⋮ Exact diagonalization of 1D interacting spinless Fermions ⋮ Source identity and kernel functions for Inozemtsev-type systems

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