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Weyl vertex algebra: Whittaker modules and fusion rules

Weyl vertex algebra (beta-gamma ghost) 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 the Weyl vertex algebra and its modules. In particular, in the first part we prove that irreducible modules of a VOA are also irreducible for its orbifolds under some conditions, and demonstrate this on the example of Whittaker modules for the Weyl vertex algebra. In the second part, we describe fusion rules in the category of weight modules for the Weyl vertex algebra 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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