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Please use this identifier to cite or link to this item: http://dspace.utalca.cl/handle/1950/10168

Title: Jack Polynomials as Fractional Quantum Hall States and the Betti Numbers of the (k+1)-Equals Ideal
Authors: Zamaere, CB.
Griffeth, S.
Sam, SV.
Keywords: RATIONAL CHEREDNIK ALGEBRAS
VARIETIES
RESOLUTIONS
MODULES
REPRESENTATION
SYMMETRIC-GROUPS
Issue Date: Aug-2014
Publisher: SPRINGER
Citation: COMMUNICATIONS IN MATHEMATICAL PHYSICS 330 (1) : 415-434
Abstract: We show that for Jack parameter alpha = -(k + 1)/(r - 1), certain Jack polynomials studied by Feigin-Jimbo-Miwa-Mukhin vanish to order r when k + 1 of the coordinates coincide. This result was conjectured by Bernevig and Haldane, who proposed that these Jack polynomials are model wavefunctions for fractional quantum Hall states. Special cases of these Jack polynomials include the wavefunctions of Laughlin and Read-Rezayi. In fact, along these lines we prove several vanishing theorems known as clustering properties for Jack polynomials in the mathematical physics literature, special cases of which had previously been conjectured by Bernevig and Haldane. Motivated by the method of proof, which in the case r = 2 identifies the span of the relevant Jack polynomials with the S (n) -invariant part of a unitary representation of the rational Cherednik algebra, we conjecture that unitary representations of the type A Cherednik algebra have graded minimal free resolutions of Bernstein-Gelfand-Gelfand type; we prove this for the ideal of the (k + 1)-equals arrangement in the case when the number of coordinates n is at most 2k + 1. In general, our conjecture predicts the graded S (n) -equivariant Betti numbers of the ideal of the (k + 1)-equals arrangement with no restriction on the number of ambient dimensions.
Description: Univ Talca, Inst Matemat & Fis, Talca, Chile. Griffeth, S (Griffeth, Stephen)
URI: http://dspace.utalca.cl/handle/1950/10168
ISSN: 1432-0916
Appears in Collections:Artículos en publicaciones ISI - Universidad de Talca

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