Search results for "Virasoro algebra"
showing 5 items of 5 documents
Kac-Moody group representations and generalization of the Sugawara construction of the Virasoro algebra
1988
We discuss the dynamical structure of the semidirect product of the Virasoro and affine Kac-Moody groups within the framework of a group quantization formalism. This formalism provides a realization of the Virasoro algebra acting on Kac-Moody Fock states which generalizes the Sugawara construction. We also give an explicit construction of the standard Kac-Moody group representations associated with strings on SU(2) and recover, in particular, the ‘renormalization’ β factor of L(z)
Indecomposable modules over the Virasoro Lie algebra and a conjecture of V. Kac
1991
We consider a class of indecomposable modules over the Virasoro Lie algebra that we call bounded admissible modules. We get results concerning the center and the dimensions of the weight spaces. We prove that these modules always contain a submodule with one-dimensional weight spaces. From this follows the proof of a conjecture of V. Kac concerning the classification of simple admissible modules.
The Virasoro Algebra
1989
In this chapter we shall study the Lie algebra Vect S1 of vector fields on a circle and some of its generalizations. The Lie algebra Vect S1 has a central extension, the Virasoro algebra. The representation theory of the Virasoro algebra is closely related to the representation theory of affine Lie algebras. In fact, through the Sugawara construction, to be defined below, a highest weight representation of an affine Lie algebra carries always a highest weight representation of the Virasoro algebra. All the irreducible highest weight representations of the Virasoro algebra are known and they can be exponentiated to representations of associated infinite-dimensional Lie groups. The representa…
Abelian current algebra and the Virasoro algebra on the lattice
1993
We describe how a natural lattice analogue of the abelian current algebra combined with free discrete time dynamics gives rise to the lattice Virasoro algebra and corresponding hierarchy of conservation laws.
Quasidisks and string theory
1990
Abstract A heuristic model of non-perturbative bosonic string theory on the Bers universal Teichmuller space of normalized quasidisks is discussed. It is suggested that the infinite-dimensional analogue of the Polyakov energy might be the quasidisk area.