Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Liouville Type Models in Group Theory Framework. I. Finite-Dimensional
  Algebras   In the series of papers we represent the ``Whittaker'' wave functional of
$d+1$-dimensional Liouville model as a correlator in $d+0$-dimensional theory
of the sine-Gordon type (for $d=0$ and $1$). Asypmtotics of this wave function
is characterized by the Harish-Chandra function, which is shown to be a product
of simple $\Gamma$-function factors over all positive roots of the
corresponding algebras (finite-dimensional for $d=0$ and affine for $d=1$).
This is in nice correspondence with the recent results on 2- and 3-point
correlators in $1+1$ Liouville model, where emergence of peculiar
double-periodicity is observed. The Whittaker wave functions of
$d+1$-dimensional non-affine ("conformal") Toda type models are given by simple
averages in the $d+0$ dimensional theories of the affine Toda type. This
phenomenon is in obvious parallel with representation of the free-field wave
functional, which is originally a Gaussian integral over interior of a
$d+1$-dimensional disk with given boundary conditions, as a (non-local)
quadratic integral over the $d$-dimensional boundary itself. In the present
paper we mostly concentrate on the finite-dimensional case. The results for
finite-dimensional "Iwasawa" Whittaker functions were known, and we present
their survey. We also construct new "Gauss" Whittaker functions.

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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: quant-ph