Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Double Macdonald polynomials as the stable limit of Macdonald
  superpolynomials   Macdonald superpolynomials provide a remarkably rich generalization of the
usual Macdonald polynomials. The starting point of this work is the observation
of a previously unnoticed stability property of the Macdonald superpolynomials
when the fermionic sector m is sufficiently large: their decomposition in the
monomial basis is then independent of m. These stable superpolynomials are
readily mapped into bisymmetric polynomials, an operation that spoils the ring
structure but drastically simplifies the associated vector space. Our main
result is a factorization of the (stable) bisymmetric Macdonald polynomials,
called double Macdonald polynomials and indexed by pairs of partitions, into a
product of Macdonald polynomials (albeit subject to non-trivial plethystic
transformations). As an off-shoot, we note that, after multiplication by a
t-Vandermonde determinant, this provides explicit formulas for a large class of
Macdonald polynomials with prescribed symmetry. The factorization of the double
Macdonald polynomials leads immediately to the generalization of basically
every elementary properties of the Macdonald polynomials to the double case
(norm, kernel, duality, positivity, etc). When lifted back to superspace, this
validates various previously formulated conjectures in the stable regime.
  The q,t-Kostka coefficients associated to the double Macdonald polynomials
are shown to be q,t-analogs of the dimensions of the irreducible
representations of the hyperoctahedral group B_n. Moreover, a Nabla operator on
the double Macdonald polynomials is defined and its action on a certain
bisymmetric Schur function can be interpreted as the Frobenius series of a
bigraded module of dimension (2n+1)^n, a formula again characteristic of the
Coxeter group of type B_n.
  Finally, as a side result, we obtain a simple identity involving products of
four Littlewood-Richardson coefficients.

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The categories of this paper are: cs
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: funct-an