A recursion and a combinatorial formula for Jack polynomials

Knop, Friedrich; Sahi, Siddhartha

doi:10.1007/s002220050134

Cited by 165 publications

(216 citation statements)

References 3 publications

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“…quotient A T N (t) of the A.H.A. generated by e i , y i where we constrain the generators e i to obey the restrictions: Following [36], one can define operators Y l which intertwine the affine generators:…”

Section: A Affine Algebrasmentioning

confidence: 99%

On Polynomials Interpolating Between the Stationary State of a O(n) Model and a Q.H.E. Ground State

Kasatani

Pasquier

2007

Commun. Math. Phys.

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We obtain a family of polynomials defined by vanishing conditions and associated to tangles. We study more specifically the case where they are related to a O(n) loop model. We conjecture that their specializations at z i = 1 are positive in n. At n = 1, they coincide with the the Razumov-Stroganov integers counting alternating sign matrices.We derive the CFT modular invariant partition functions labelled by CoxeterDynkin diagrams using the representation theory of the affine Hecke algebras.

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Section: A Affine Algebrasmentioning

confidence: 99%

On Polynomials Interpolating Between the Stationary State of a O(n) Model and a Q.H.E. Ground State

Kasatani

Pasquier

2007

Commun. Math. Phys.

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“…The starting point is not anymore the extension of the usual Jack polynomial eigenvalue problem, but rather a symmetrization process performed on the non-symmetric Jack polynomials [6,7], suitably dressed with products of fermionic variables.…”

Section: Introductionmentioning

confidence: 99%

Jack Polynomials in Superspace

Desrosiers

Lapointe

Mathieu

2003

Commun. Math. Phys.

113

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This work initiates the study of orthogonal symmetric polynomials in superspace. Here we present two approaches leading to a family of orthogonal polynomials in superspace that generalize the Jack polynomials. The first approach relies on previous work by the authors in which eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland Hamiltonian were constructed. Orthogonal eigenfunctions are now obtained by diagonalizing the first nontrivial element of a bosonic tower of commuting conserved charges not containing this Hamiltonian. Quite remarkably, the expansion coefficients of these orthogonal eigenfunctions in the supermonomial basis are stable with respect to the number of variables. The second and more direct approach amounts to symmetrize products of non-symmetric Jack polynomials with monomials in the fermionic variables. This time, the orthogonality is inherited from the orthogonality of the non-symmetric Jack polynomials, and the value of the norm is given explicitly. *

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“…On the mathematical side, explicit expressions for the Jack polynomials have been obtained using a non-symmetric version of these polynomials [36]. And more recently, a rather simple determinant formula for the Jack polynomials has been presented [37].…”

Section: Introductionmentioning

confidence: 99%

Supersymmetric Calogero–Moser–Sutherland models and Jack superpolynomials

2001

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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.

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A recursion and a combinatorial formula for Jack polynomials

Cited by 165 publications

References 3 publications

On Polynomials Interpolating Between the Stationary State of a O(n) Model and a Q.H.E. Ground State

On Polynomials Interpolating Between the Stationary State of a O(n) Model and a Q.H.E. Ground State

Jack Polynomials in Superspace

Supersymmetric Calogero–Moser–Sutherland models and Jack superpolynomials

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