Sekiguchi-Debiard operators at infinity

DOI10.1007/s00220-013-1821-zzbMath1408.81016arXiv1212.2781OpenAlexW2152768977WikidataQ59721847 ScholiaQ59721847MaRDI QIDQ387643

M. L. Nazarov, Evgueni K. Sklyanin

Publication date: 23 December 2013

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

Full work available at URL: https://arxiv.org/abs/1212.2781

Mathematics Subject Classification ID

Symmetric functions and generalizations (05E05) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Many-body theory; quantum Hall effect (81V70) Generalized hypergeometric series, ({}_pF_q) (33C20) Operator algebra methods applied to problems in quantum theory (81R15) Orthogonal polynomials and functions associated with root systems (33C52)

Related Items (16)

Spectral theory of the Nazarov-Sklyanin Lax operator ⋮ Macdonald operators at infinity ⋮ Deformed Calogero-Sutherland model and fractional quantum Hall effect ⋮ On spin Calogero–Moser system at infinity ⋮ Finite gap conditions and small dispersion asymptotics for the classical periodic Benjamin–Ono equation ⋮ The Spin Calogero-Sutherland Model at Infinity ⋮ Free field theory and observables of periodic Macdonald processes ⋮ Interpolation Macdonald operators at infinity ⋮ Free field approach to the Macdonald process ⋮ Exact Bohr-Sommerfeld conditions for the quantum periodic Benjamin-Ono equation ⋮ Instanton R-matrix and \(\mathcal{W}\)-symmetry ⋮ Fermionic limit of the Calogero-Sutherland system ⋮ On Cherednik and Nazarov-Sklyanin large N limit construction for integrable many-body systems with elliptic dependence on momenta ⋮ Jack–Laurent symmetric functions ⋮ Matrix elements of vertex operators and fermionic limit of spin Calogero-Sutherland system ⋮ Lax operator for Macdonald symmetric functions

Cites Work

• Cherednik algebras, \(W\)-algebras and the equivariant cohomology of the moduli space of instantons on \(\mathbb A^2\)
• Macdonald operators at infinity
• Applications of a Laplace-Beltrami operator for Jack polynomials
• Quantum cohomology of the Hilbert scheme of points in the plane
• A family of integral transformations and basic hypergeometric series
• Gromov-Witten invariants of target curves via symplectic field theory
• Zonal spherical functions on some symmetric spaces
• Collective field theory, Calogero-Sutherland model and generalized matrix models
• Exact operator solution of the Calogero-Sutherland model
• Irreducible representations of Yangians
• Macdonald operators and homological invariants of the colored Hopf link
• Waves and Solitons in the Continuum Limit of the Calogero-Sutherland Model
• Boson-fermion correspondence and quantum integrable and dispersionless models
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