Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weyl group multiple Dirichlet series of type C   We develop the theory of Weyl group multiple Dirichlet series for root
systems of type C. For an arbitrary root system of rank r and a positive
integer n, these are Dirichlet series in r complex variables with analytic
continuation and functional equations isomorphic to the associated Weyl group.
In type C, they conjecturally arise from the Fourier-Whittaker coefficients of
minimal parabolic Eisenstein series on an n-fold metaplectic cover of SO(2r+1).
For any odd n, we construct an infinite family of Dirichlet series
conjecturally satisfying the above analytic properties. The coefficients of
these series are exponential sums built from Gelfand-Tsetlin bases of certain
highest weight representations. Previous attempts to define such series by
Brubaker, Bump, and Friedberg in [6] and [7] required n to be sufficiently
large, so that coefficients could be described by Weyl group orbits. We
demonstrate that our construction agrees with that of [6] and [7] in the case
where both series are defined, and hence inherits the desired analytic
properties for n sufficiently large. Moreover our construction is valid even
for n=1, where we prove our series is a Whittaker coefficient of an Eisenstein
series. This requires the Casselman-Shalika formula for unramified principal
series and a remarkable deformation of the Weyl character formula of Hamel and
King [20].

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The categories of this paper are: hep-lat
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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-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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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: astro-ph