Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A combinatorial formula for Sahi, Stokman, and Venkateswaran's
  generalization of Macdonald polynomials   Sahi, Stokman, and Venkateswaran have constructed, for each positive integer
$n$, a family of Laurent polynomials depending on parameters $q$ and $k$ (in
addition to $\lfloor n/2\rfloor$ "metaplectic parameters"), such that the $n=1$
case recovers the nonsymmetric Macdonald polynomials and the
$q\rightarrow\infty$ limit yields metaplectic Iwahori-Whittaker functions with
arbitrary Gauss sum parameters. In this paper, we study these new polynomials,
which we call SSV polynomials, in the case of $GL_r$. We apply a result of Ram
and Yip in order to give a combinatorial formula for the SSV polynomials in
terms of alcove walks. The formula immediately shows that the SSV polynomials
satisfy a triangularity property with respect to a version of the Bruhat order,
which in turn gives an independent proof that the SSV polynomials are a basis
for the space of Laurent polynomials. The result is also used to show that the
SSV polynomials have \emph{fewer} terms than the corresponding Macdonald
polynomials. We also record an alcove walk formula for the natural
generalization of the permuted basement Macdonald polynomials. We then
construct a symmetrized variant of the SSV polynomials: these are symmetric
with respect to a conjugate of the Chinta-Gunnells Weyl group action and reduce
to symmetric Macdonald polynomials when $n=1$. We obtain an alcove walk formula
for the symmetrized polynomials as well. Finally, we calculate the
$q\rightarrow 0$ and $q\rightarrow \infty$ limits of the SSV polynomials and
observe that our combinatorial formula can be written in terms of alcove walks
with only positive and negative folds respectively. In both of these $q$-limit
cases, we also observe a positivity result for the coefficients.

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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th