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βγ ghosts: Whittaker modules and fusion rules

The bosonic ghost vertex algebra (beta-gamma ghosts) is an important object both in physics (string theory) and in mathematics (representation theory), arising as a module for the Weyl associative algebra. In this talk we give some information on beta-gamma ghosts and their modules. In particular, in the first part we prove that irreducible modules of a VOA are also irreducible for orbifolds under some conditions, and demonstrate this on the example of Whittaker modules for bosonic ghosts. In the second part, we describe fusion rules in the category of weight modules for the beta-gamma ghost and explicitly construct the associated intertwining operators. This talk is based on two papers, first one joint with D. Adamovic, C.-H. Lam and N. Yu, and the second one with D. Adamovic.

Vertex algebras, vertex operator algebras, fusion rules, intertwining operators, Lie superalgebra

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