Liouville type models in the group theory framework: I. Finite-dimensional algebras

A. Gerasimov, S. Kharchev, A. Morozov, M. Olshanetsky, A. Marshakov, A. Mironov

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)


In this series of papers we represent the "Whittaker" wave functional of the (d + 1)-dimensional Liouville model as a correlator in (d + 0)-dimensional theory of the sine-Gordon type (for d = 0 and 1). The asymptotics of this wave function is characterized by the Harish-Chandra function, which is shown to be a product of simple Γ 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 two-and three-point correlators in the 1 + 1 Liouville model, where emergence of peculiar double periodicity is observed. The Whittaker wave functions of (d + 1)-dimensional nonaffine ("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 was originally a Gaussian integral over the interior of a (d + 1)-dimensional disk with given boundary conditions, as a (nonlocal) quadratic integral over the d-dimensional boundary itself. In this paper we concentrate on the finite-dimensional case. The results for finite-dimensional "Iwasawa" Whittaker functions are known, and we present a survey. We also construct new "Gauss" Whittaker functions.

Original languageEnglish
Pages (from-to)2523-2583
Number of pages61
JournalInternational Journal of Modern Physics A
Issue number14
Publication statusPublished - 10 Jun 1997
Externally publishedYes


Dive into the research topics of 'Liouville type models in the group theory framework: I. Finite-dimensional algebras'. Together they form a unique fingerprint.

Cite this