Representation theory of the stabilizer subgroup of the point at infinity in Diff(S^1)

Details Representation theory of the stabilizer subgroup of the point at infinity in Diff(S^1) Representation theory of the stabilizer subgroup of the point at infinity in Diff(S^1)

2009-05-06

arxiv.org/abs/0905.0875v3

Internat. J. Math., Vol. 21, No. 10 (2010), 1297-1335

Physics

Mathematical Physics

34 pages, no figure

Scientific paper

10.1142/S0129167X10006525

The group Diff(S^1) of the orientation preserving diffeomorphisms of the circle S^1 plays an important role in conformal field theory. We consider a subgroup B_0 of Diff(S^1) whose elements stabilize "the point of infinity". This subgroup is of interest for the actual physical theory living on the punctured circle, or the real line. We investigate the unique central extension K of the Lie algebra of that group. We determine the first and second cohomologies, its ideal structure and the automorphism group. We define a generalization of Verma modules and determine when these representations are irreducible. Its endomorphism semigroup is investigated and some unitary representations of the group which do not extend to Diff(S^1) are constructed.

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