AN-type Dunkl operators and new spin Calogero–Sutherland models
نویسندگان
چکیده
A new family of AN -type Dunkl operators preserving a polynomial subspace of finite dimension is constructed. Using a general quadratic combination of these operators and the usual Dunkl operators, several new families of exactly and quasi-exactly solvable quantum spin Calogero–Sutherland models are obtained. These include, in particular, three families of quasi-exactly solvable elliptic spin Hamiltonians.
منابع مشابه
B N - type Dunkl operators
We construct several new families of exactly and quasi-exactly solvable BCN -type Calogero– Sutherland models with internal degrees of freedom. Our approach is based on the introduction of a new family of Dunkl operators of BN type which, together with the original BN -type Dunkl operators, are shown to preserve certain polynomial subspaces of finite dimension. We prove that a wide class of qua...
متن کاملar X iv : m at h - ph / 0 40 90 48 v 1 1 9 Se p 20 04 1 Equivalence of the super Lax and local Dunkl operators for Calogero - like models
Following Shastry and Sutherland I construct the super Lax operators for the Calogero model in the oscillator potential. These operators can be used for the derivation of the eigenfunctions and integrals of motion of the Calogero model and its supersymmetric version. They allow to infer several relations involving the Lax matrices for this model in a fast way. It is shown that the super Lax ope...
متن کاملCommon Algebraic Structure for the Calogero-Sutherland Models
We investigate common algebraic structure for the rational and trigonometric Calogero-Sutherland models by using the exchange-operator formalism. We show that the set of the Jack polynomials whose arguments are Dunkl-type operators provide an orthogonal basis for the rational case. One dimensional quantum integrable models with long-range interaction have attracted much interest, because of not...
متن کاملSupersymmetric Calogero-Moser-Sutherland models and Jack superpolynomials
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 ne...
متن کاملThree-body generalization of the Sutherland model with internal degrees of freedom
A generalized spin Sutherland model including a three-body potential is proposed. The problem is analyzed in terms of three first-order differential-difference operators, obtained by combining SUSYQM supercharges with the elements of the dihedral group D6. Three alternative commuting operators are also introduced. PACS: 03.65.Fd, 02.20.Df, 11.30.Pb Directeur de recherches FNRS; E-mail: cquesne@...
متن کامل