1 9 A ug 2 00 9 TRANSLATION FOR FINITE W - ALGEBRAS
نویسنده
چکیده
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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