The Steinberg variety and representations of reductive groups
نویسندگان
چکیده
منابع مشابه
The Steinberg Variety and Representations of Reductive Groups
We give an overview of some of the main results in geometric representation theory that have been proved by means of the Steinberg variety. Steinberg’s insight was to use such a variety of triples in order to prove a conjectured formula by Grothendieck. The Steinberg variety was later used to give an alternative approach to Springer’s representations and played a central role in the proof of th...
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Let F be either R or a finite extension of Qp, and let G be a finite central extension of the group of F -points of a reductive group defined over F . Also let π be a smooth representation of G (Fréchet of moderate growth if F = R). For each nilpotent orbit O we consider a certain Whittaker quotient πO of π. We define the Whittaker support WS(π) to be the set of maximal O among those for which ...
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is continuous. “Locally convex” means that the space has lots of continuous linear functionals, which is technically fundamental. “Complete” allows us to take limits in V , and so define things like integrals and derivatives. The representation (π, V ) is irreducible if V has exactly two closed invariant subspaces (which are necessarily 0 and V ). The representation (π, V ) is unitary if V is a...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2009
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2008.10.027