Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Jack polynomials as fractional quantum Hall states and the Betti numbers
  of the (k+1)-equals ideal   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 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.

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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: nucl-ex
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: econ