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Title of Journal: Sel. Math. New Ser.

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Abbravation: Selecta Mathematica

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Springer Basel

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10.1007/11687061_1

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1420-9020

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Geometric Satake, Springer correspondence and small representations

Authors: Pramod N. Achar, Anthony Henderson,

Publish Date: 2013/05/05
Volume: 19, Issue:4, Pages: 949-986
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Abstract

For a simply-connected simple algebraic group \(G\) over \(\mathbb C \), 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.This paper developed from discussions with V. Ginzburg and S. Riche, to whom the authors are much indebted. In particular, V. Ginzburg posed the problem of finding a geometric interpretation of Broer’s covariant theorem in the context of geometric Satake. Much of the work was carried out during a visit by P.A. to the University of Sydney in May–June 2011, supported by ARC Grant No. DP0985184. P.A. also received support from NSF Grant No. DMS-1001594.


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