Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Macdonald Polynomials from Sklyanin Algebras: A Conceptual Basis for the
  $p$-Adics-Quantum Group Connection   We establish a previously conjectured connection between $p$-adics and
quantum groups. We find in Sklyanin's two parameter elliptic quantum algebra
and its generalizations, the conceptual basis for the Macdonald polynomials,
which ``interpolate'' between the zonal spherical functions of related real and
$p$\--adic symmetric spaces. The elliptic quantum algebras underlie the
$Z_n$\--Baxter models. We show that in the $n \air \infty$ limit, the Jost
function for the scattering of {\em first} level excitations in the
$Z_n$\--Baxter model coincides with the Harish\--Chandra\--like $c$\--function
constructed from the Macdonald polynomials associated to the root system $A_1$.
The partition function of the $Z_2$\--Baxter model itself is also expressed in
terms of this Macdonald\--Harish\--Chandra\ $c$\--function, albeit in a less
simple way. We relate the two parameters $q$ and $t$ of the Macdonald
polynomials to the anisotropy and modular parameters of the Baxter model. In
particular the $p$\--adic ``regimes'' in the Macdonald polynomials correspond
to a discrete sequence of XXZ models. We also discuss the possibility of
``$q$\--deforming'' Euler products.

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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an