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The idea of explaining [10] using geometric Satake was suggested to us by Ginzburg; the idea of explaining [27] using perverse sheaves on the affine Grassmannian was suggested to Reeder by Lusztig, as mentioned in [28]. Let Gr and N denote the affine Grassmannian and the nilpotent cone of G, respec-tively, and consider the diagram Rep(Gˇ ...
Notes on the Geometric Satake Equivalence Pierre Baumann and Simon Riche 1.1 Introduction 1.1.1 Description These notes are devoted to a detailed exposition of the proof of the Geometric Satake Equivalence for general coefficients by Mirkovi´c–Vilonen [ MV3]. This celebrated result provides, for G a complex connected reductive algebraic group
5 de nov. de 2013 · I extend the ramified geometric Satake equivalence of Zhu from tamely ramified groups to include the case of general connected reductive groups. As a prerequisite I prove basic results on the geometry of affine flag varieties.
2 Geometric Satake Correspondence Today, we will go over all of the necessary ingredients in the Geometric Satake Correspondence that we will need next time. Theorem 1 (Geometric Satake Correspondence). Let Gbe a complex reductive group, kbe a Noetherian ring of finite global dimension, and denoteG∨ k as the Langlands dual of Gover k.
1. The category of smooth representations of G K is equivalent to the category. ( ) of smooth regular modules V over H G - i.e. such that H G · V V and each vector is fixed. ( ) ( ) =. under the action of an indicator function 1U for an open subgroup U ⊆ G K . ( ) 2. For every fixed open compact subgroup U ⊆ G the map.
GEOMETRIC SATAKE CORRESPONDENCE 1. Overview (notes by Michael Zhao)2 1.1. Next Few Weeks2 1.2. Course Overview2 2. Representation and Structure Theory of Compact Lie Groups (notes by Michael Zhao) 3 2.1. Lie Algebras4 2.2. Exponential Map4 2.3. Representation of Compact Lie Groups5 2.4. Onto Representation Theory6 2.5. The Representation Ring8 3.
23 de mar. de 2022 · Fargues and Scholze proved the geometric Satake equivalence over the Fargues--Fontaine curve. On the other hand, Zhu proved the geometric Satake equivalence using a Witt vector affine Grassmannian. In this paper, we explain the relation between the two version of the geometric Satake equivalence via nearby cycle.
