Liouville type models in group theory framework. 1. Finite dimensional algebras
Jan, 1996
46 pages
Published in:
- Int.J.Mod.Phys.A 12 (1997) 2523-2584
e-Print:
- hep-th/9601161 [hep-th]
Report number:
- ITEP-M4-TH-7-95,
- FIAN-TD-18-95,
- ITEP-TH-7-95
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Abstract:
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.Note:
- 47 pages, LaTeX
- field theory: Liouville
- group theory: SL(N)
- group theory: representation
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