Geometric Satake Springer correspondence and smal

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 simplyconnected 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 wellknown fact about GL n Using this variety we construct a sheaftheoretic 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 groupThis 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 PA to the University of Sydney in May–June 2011 supported by ARC Grant No DP0985184 PA also received support from NSF Grant No DMS1001594

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