Operator coproduct-realization of quantum group transformations in two-dimensional gravity I |
| |
Authors: | Eugène Cremmer Jean-Loup Gervais Jens Schnittger |
| |
Institution: | (1) Laboratoire de Physique Théorique de l'Ecole Normale Supérieure, 24 rue Lhomond, F-75231 Paris Cedex 05, France;(2) Present address: CERN Theory Division, CH-1211 Geneva 23, Switzerland |
| |
Abstract: | A simple connection between the universalR matrix ofU
q(sl(2)) (for spins 1/2 andJ) and the required form of the coproduct action of the Hilbert space generators of the quantum group symmetry is put forward. This leads us to an explicit operator realization of the coproduct action on the covariant operators. It allows us to derive the expected quantum group covariance of the fusion and braiding matrices, although it is of a new type: the generators depend upon worldsheet variables, and obey a new central extension of theU
q(sl(2)) algebra realized by (what we call) fixed point commutation relations. This is explained by showing on a general ground that the link between the algebra of field transformations and that of the coproduct generators is much weaker than previously thought. The central charges of our extendedU
q(sl(2)) algebra, which includes the Liouville zero-mode momentum in a non-trivial way, are related to Virasoro-descendants of unity. We also show how our approach can be used to derive the Hopf algebra structure of the extended quantum-group symmetry related to the presence of both of the screening charges of 2D gravity.Partially supported by the EC contracts CHRXCT920069 and CHRXCT920035.Unité Propre du Centre National de la Recherche Scientifique, associée à l'École Normale Supérieure et à l'Université de Paris-Sud. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|