Supersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials

Abstract

A new generalization of the Jack polynomials that incorporates fermionic variables is presented. These Jack superpolynomials are constructed as those eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland (CMS) model that decomposes triangularly in terms of the symmetric monomial superfunctions. Many explicit examples are displayed. Furthermore, various new results have been obtained for the supersymmetric version of the CMS models: the Lax formulation, the construction of the Dunkl operators and the explicit expressions for the conserved charges. The reformulation of the models in terms of the exchange-operator formalism is a crucial aspect of our analysis.

Minor corrections in tables; 30 pages

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Cited by in corpus (36)

• Orthogonality of Jack polynomials in superspace
• Superconformal field theory and Jack superpolynomials
• The supersymmetric Ruijsenaars-Schneider model
• Jack polynomials in superspace
• Evaluation and normalization of Jack superpolynomials
• Classical symmetric functions in superspace
• Supersymmetric hyperbolic Calogero-Sutherland models by gauging
• Macdonald polynomials in superspace: conjectural definition and positivity conjectures
• Generalized Hermite polynomials in superspace as eigenfunctions of the supersymmetric rational CMS model
• Intertwining Relations for the Matrix Calogero-like Models: Supersymmetry and Shape Invariance
• Super-Calogero model with OSp(2|2) supersymmetry : is the construction unique?
• Superconformal minimal models and admissible Jack polynomials
• Yangian associated with 2D $\mathcal{N}=1$ SCFT
• Supersymmetric Extensions of Calogero--Moser--Sutherland like Models: Construction and Some Solutions
• Solvable scalar and spin models with near-neighbors interactions
• Admissible level $\mathfrak{osp}(1|2)$ minimal models and their relaxed highest weight modules
• On $\mathcal{N}=2$ supersymmetric Ruijsenaars-Schneider models
• Explicit formulas for the generalized Hermite polynomials in superspace
• Supersymmetric Many-particle Quantum Systems with Inverse-square Interactions
• Exchange operator formalism for N-body spin models with near-neighbors interactions
• Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals
• $\mathcal{N}=2$ supersymmetric hyperbolic Calogero-Sutherland model
• Schur Superpolynomials: Combinatorial Definition and Pieri Rule
• Supersymmetry and Models for Two Kinds of Interacting Particles
• Algebra of the observables in the Calogero model and in the Chern-Simons matrix model
• Ramond singular vectors and Jack superpolynomials
• Singular vectors for the $W_N$ algebras
• From Jack to Double Jack Polynomials via the Supersymmetric Bridge
• Supersymmetric Hamiltonian Approach to Edge Excitations in $\nu =5/2$ Fractional Quantum Hall Effect
• Bernstein operators and super-Schur functions: combinatorial aspects
• New $\mathcal{N}=2$ superspace Calogero models
• Supersymmetric Calogero models from superfield gauging
• A Superpolynomial Version of Nonsymmetric Jack Polynomials
• Symmetric functions in noncommuting variables in superspace
• Integrability of supersymmetric Calogero-Moser models
• Equivalence of the super Lax and local Dunkl operators for Calogero-like models