##  [Satake Isomorphism](/satake-isomorphism) 

  ##  [Satake Isomorphism](https://algebra.quantumdictionary.io/satake-isomorphism-0) 

  

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- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

An algebra isomorphism in the representation theory of reductive p-adic groups identifying the spherical Hecke algebra of bi-K-invariant compactly supported functions (or its convolution algebra) with the coordinate ring (or representation ring) of the complex torus attached to the Langlands dual group restricted to W-invariants, thereby linking harmonic analysis on the p-adic side to algebraic fu