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Title:
Generalized and degenerate Whittaker models for representations of reductive groups
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Abstract:
A Whittaker pair is a pair (S,f) of elements of the Lie algebra of a reductive group G such that S is semi-simple and [S,f]=-2f. To any Whittaker pair one associates a degenerate Whittaker model. Given a nilpotent element f, one can always complete it to a Whittaker pair using the Jacobson-Morozov theorem. I will show the advantage of considering also other kinds of Whittaker pairs, and present some recent results, j.w. S. Sahi and R. Gomez, on the connection between degenerate Whittaker models corresponding to Whittaker pairs with the same nilpotent component. I will also discuss a related question: given a smooth representation $\pi$ of G, what are the maximal (with respect to the closure partial ordering) nilpotent orbits O such that $\pi$ has a degenerate Whittaker model with respect to some Whittaker pair (S,f) with f lying in O?
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