Search results for "17B68"

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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.

Discrete mathematicsPure mathematics17B10Statistical and Nonlinear PhysicsUniversal enveloping algebraLie superalgebraAffine Lie algebra17B68Lie conformal algebraGraded Lie algebraAlgebra representationVirasoro algebraMathematics::Representation TheoryIndecomposable moduleMathematical PhysicsMathematicsCommunications in Mathematical Physics
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Quantization on the Virasoro group

1990

The quantization of the Virasoro group is carried out by means of a previously established group approach to quantization. We explicitly work out the two-cocycles on the Virasoro group as a preliminary step. In our scheme the carrier space for all the Virasoro representations is made out of polarized functions on the group manifold. It is proved that this space does not contain null vector states, even forc≦1, although it is not irreducible. The full reduction is achieved in a striaghtforward way by just taking a well defined invariant subspace ℋ(c, h), the orbit of the enveloping algebra through the vacuum, which is irreducible for any value ofc andh. ℋ(c, h) is a proper subspace of the sp…

Pure mathematicsGroup (mathematics)Quantization (signal processing)Invariant subspaceStatistical and Nonlinear Physics81S10ManifoldGroup representation17B68Algebra58F06Null vector81R10Algebra representation22E65Mathematical PhysicsSymplectic geometryMathematics
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