Calogero operator and Lie superalgebras

DOI10.1023/A:1015968505753zbMath1039.81028OpenAlexW1587747180MaRDI QIDQ1417379

Alexander Sergeev

Publication date: 4 January 2004

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1015968505753

zbMATH Keywords

Lie superalgebraspherical functionJack polynomialsymmetric superspaceCalogero operator

Mathematics Subject Classification ID

Groups and algebras in quantum theory and relations with integrable systems (81R12) Supersymmetry and quantum mechanics (81Q60) Applications of Lie algebras and superalgebras to integrable systems (17B80)

Related Items (20)

\(\mathcal{N} = 4\) supersymmetric U(2)-spin hyperbolic Calogero-Sutherland model ⋮ Symmetric Lie superalgebras and deformed quantum Calogero-Moser problems ⋮ Brownian-motion ensembles of random matrix theory: a classification scheme and an integral transform method ⋮ Source identities and kernel functions for deformed (quantum) Ruijsenaars models ⋮ Generalized Calogero-Moser systems from rational Cherednik algebras ⋮ New orthogonality relations for super-Jack polynomials and an associated Lassalle-Nekrasov correspondence ⋮ Deformed Calogero-Sutherland model and fractional quantum Hall effect ⋮ \(\mathcal{N} = 2\) supersymmetric hyperbolic Calogero-Sutherland model ⋮ Series solutions of the non-stationary Heun equation ⋮ Lie superalgebras and Calogero-Moser-Sutherland systems ⋮ A unified construction of generalized classical polynomials associated with operators of Calogero-Sutherland type ⋮ Generalised discriminants, deformed Calogero-Moser-Sutherland operators and super-Jack polynomials ⋮ Source identity and kernel functions for elliptic Calogero-Sutherland type systems ⋮ Supersymmetric hyperbolic Calogero-Sutherland models by gauging ⋮ Intertwining operator for AG2 Calogero–Moser–Sutherland system ⋮ Orthogonality of super‐Jack polynomials and a Hilbert space interpretation of deformed Calogero–Moser–Sutherland operators ⋮ From Kajihara's transformation formula to deformed Macdonald-Ruijsenaars and Noumi-Sano operators ⋮ Source identities and kernel functions for the deformed Koornwinder-van Diejen models ⋮ Source identity and kernel functions for Inozemtsev-type systems ⋮ Eigenfunctions of the van Diejen model generated by gauge and integral transformations

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