##  [Geometric Satake Correspondence](/geometric-satake-correspondence) 

  ##  [Geometric Satake Correspondence](https://algebra.quantumdictionary.io/geometric-satake-correspondence-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A categorical equivalence that upgrades the Satake isomorphism: it identifies the tensor category of G(O)-equivariant perverse sheaves (or suitably defined Satake category) on the affine Grassmannian of a reductive group G with the tensor category of algebraic representations of the Langlands dual group G^∨, realizing the dual group and its representations geometrically.