3 research outputs found
Liouville Type Models in Group Theory Framework. I. Finite-Dimensional Algebras
In the series of papers we represent the ``Whittaker'' wave functional of
-dimensional Liouville model as a correlator in -dimensional theory
of the sine-Gordon type (for and ). Asypmtotics of this wave function
is characterized by the Harish-Chandra function, which is shown to be a product
of simple -function factors over all positive roots of the
corresponding algebras (finite-dimensional for and affine for ).
This is in nice correspondence with the recent results on 2- and 3-point
correlators in Liouville model, where emergence of peculiar
double-periodicity is observed. The Whittaker wave functions of
-dimensional non-affine ("conformal") Toda type models are given by simple
averages in the 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
-dimensional disk with given boundary conditions, as a (non-local)
quadratic integral over the -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.Comment: 47 pages, LaTe