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Generalised discriminants, deformed CalogeroMoserSutherland operators and superJack polynomials
 ADV. MATH
"... It is shown that the deformed CalogeroMoserSutherland (CMS) operators can be described as the restrictions on certain affine subvarieties of the usual CMS operators for infinite number of particles. The ideals of these varieties are shown to be generated by the Jack symmetric functions related to ..."
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Cited by 7 (0 self)
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It is shown that the deformed CalogeroMoserSutherland (CMS) operators can be described as the restrictions on certain affine subvarieties of the usual CMS operators for infinite number of particles. The ideals of these varieties are shown to be generated by the Jack symmetric functions related
A BASIS FOR THE POLYNOMIAL EIGENFUNCTIONS OF DEFORMED CALOGEROMOSERSUTHERLAND OPERATORS
, 2008
"... ..."
Veselov Generalised discriminants, deformed CalogeroMoserSutherland operators and superJack polynomials
 Adv. Math
"... Abstract. It is shown that the deformed CalogeroMoserSutherland (CMS) operators can be described as the restrictions on certain affine subvarieties (called generalised discriminants) of the usual CMS operators for infinite number of particles. The ideals of these varieties are shown to be generate ..."
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Cited by 10 (5 self)
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Abstract. It is shown that the deformed CalogeroMoserSutherland (CMS) operators can be described as the restrictions on certain affine subvarieties (called generalised discriminants) of the usual CMS operators for infinite number of particles. The ideals of these varieties are shown
The CalogeroSutherland Model And Generalized Classical Polynomials
 Comm. Math. Phys
, 1997
"... this paper. The first is the discussion of some mathematical properties relating to the eigenfunctions, while the second is the evaluation of the density in the ground state and the exact solution of (1.6) for certain initial conditions. These problems are in fact interrelated; we find that the den ..."
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Cited by 97 (13 self)
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that the density for each system can be written in terms of a certain eigenstate and that a summation theorem for the eigenstates gives an exact solution of (1.6). A feature of the Schrodinger operators (1.2) is that after conjugation with the ground state: \Gamma e i @ \Gamma fi @W (1
the trigonometric CalogeroSutherland
, 2001
"... An elementary construction of lowering and raising operators for ..."
Trigonometric solutions of WDVV equations and generalized Calogero–Moser–Sutherland systems
"... doi:10.3842/SIGMA.2009.088 Abstract. We consider trigonometric solutions of WDVV equations and derive geometric conditions when a collection of vectors with multiplicities determines such a solution. We incorporate these conditions into the notion of trigonometric Veselov system (∨system) and we de ..."
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Cited by 4 (0 self)
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determine all trigonometric ∨systems with up to five vectors. We show that generalized Calogero–Moser–Sutherland operator admits a factorized eigenfunction if and only if it corresponds to the trigonometric ∨system; this inverts a oneway implication observed by Veselov for the rational solutions.
A lecture on the CalogeroSutherland models.
"... INTRODUCTION The CalogeroSutherland model has recently attracted some attention mainly because, in spite of its simplicity, it yields nontrivial results which contribute to shape our understanding of fractional statistics [1]. Its most remarkable property is that its ground state is given by a Jas ..."
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INTRODUCTION The CalogeroSutherland model has recently attracted some attention mainly because, in spite of its simplicity, it yields nontrivial results which contribute to shape our understanding of fractional statistics [1]. Its most remarkable property is that its ground state is given by a
Threebody Generalizations of the Sutherland Problem
, 1997
"... The threeparticle Hamiltonian obtained by replacing the twobody trigonometric potential of the Sutherland problem by a threebody one of a similar form is shown to be exactly solvable. When written in appropriate variables, its eigenfunctions can be expressed in terms of Jack symmetric polynomials. ..."
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The threeparticle Hamiltonian obtained by replacing the twobody trigonometric potential of the Sutherland problem by a threebody one of a similar form is shown to be exactly solvable. When written in appropriate variables, its eigenfunctions can be expressed in terms of Jack symmetric polynomials
SUPERCOHERENT STATES OF CALOGEROSUTHERLAND OSCILLATOR
, 2008
"... Supersymmetric quantum mechanical model of CalogeroSutherlend singular oscillator is constructed. Supercoherent states are defined with the help of supergroup displacement operator. They are proper states of a fermionic annihilation operator. Their coordinate and superholomorphic representations ar ..."
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Supersymmetric quantum mechanical model of CalogeroSutherlend singular oscillator is constructed. Supercoherent states are defined with the help of supergroup displacement operator. They are proper states of a fermionic annihilation operator. Their coordinate and superholomorphic representations
The CalogeroSutherland Model And Polynomials With Prescribed Symmetry
 Nucl. Phys. B
, 1997
"... Introduction The Schrodinger operator + fi(fi=2 \Gamma 1) ; 0 x j L (1.1) describes quantum particles on a line of length L interacting through a 1=r pair potential with periodic boundary conditions, or equivalently quantum particles on a circle of circumference length L (h ..."
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Cited by 24 (6 self)
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Introduction The Schrodinger operator + fi(fi=2 \Gamma 1) ; 0 x j L (1.1) describes quantum particles on a line of length L interacting through a 1=r pair potential with periodic boundary conditions, or equivalently quantum particles on a circle of circumference length L
Results 1  10
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143