Translation for finite W-algebras

Details Translation for finite W-algebras Translation for finite W-algebras

2009-08-19

arxiv.org/abs/0908.2739v1

Mathematics

Representation Theory

38 pages

Scientific paper

A finite $W$-algebra $U(\g,e)$ is a certain finitely generated algebra that can be viewed as the enveloping algebra of the Slodowy slice to the adjoint orbit of a nilpotent element $e$ of a complex reductive Lie algebra $\g$. It is possible to give the tensor product of a $U(\g,e)$-module with a finite dimensional $U(\g)$-module the structure of a $U(\g,e)$-module; we refer to such tensor products as translations. In this paper, we present a number of fundamental properties of these translations, which are expected to be of importance in understanding the representation theory of $U(\g,e)$.

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