Geometric Satake, Springer correspondence, and small representations

Details Geometric Satake, Springer correspondence, and small representations Geometric Satake, Springer correspondence, and small representations

2011-08-25

arxiv.org/abs/1108.4999v1

Mathematics

Representation Theory

34 pages

Scientific paper

For a simply-connected simple algebraic group $G$ over $\C$, we exhibit a subvariety of its affine Grassmannian that is closely related to the nilpotent cone of $G$, generalizing a well-known fact about $GL_n$. Using this variety, we construct a sheaf-theoretic functor that, when combined with the geometric Satake equivalence and the Springer correspondence, leads to a geometric explanation for a number of known facts (mostly due to Broer and Reeder) about small representations of the dual group.

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