Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric Satake, Springer correspondence, and small representations II   For a split reductive group scheme $G$ over a commutative ring $k$ with Weyl
group $W$, there is an important functor $Rep(G,k) \to Rep(W,k)$ defined by
taking the zero weight space. We prove that the restriction of this functor to
the subcategory of small representations has an alternative geometric
description, in terms of the affine Grassmannian and the nilpotent cone of the
Langlands dual group to $G$. The translation from representation theory to
geometry is via the Satake equivalence and the Springer correspondence. This
generalizes the result for the $k=\mathbb{C}$ case proved by the first two
authors, and also provides a better explanation than in that earlier paper,
since the current proof is uniform across all types.

24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph