Mathematics – Representation Theory
Scientific paper
2006-12-16
Mathematics
Representation Theory
19 pages, minor corrections and up-dates, the new version is accepted for publication
Scientific paper
We prove that all finite W-algebras associated with nilpotent elements e in a complex semisimple Lie algebra g have finite-dimensional representations. In order to obtain this result we establish a connection between primitive ideals of U(g) attached to the nilpotent orbit containing e and finite-dimensional representations of the reduced enveloping algebra assiciated with e over an algebraically closed field of finite characteristic.
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