nLab
geometric Satake equivalence

Contents

Idea

The geometric Satake equivalence identifies for a suitable algebraic group GG, and suitable local field KK with ring of integers 𝒪 K\mathcal{O}_K, suitable functions on the double coset/Grassmannian G(𝒪 K)\G(K)/G(𝒪 K)G(\mathcal{O}_K)\backslash G(K)/G(\mathcal{O}_K) with the representation ring of the Langlands dual group LG{}^L G.

Notice that the double coset appearing here is akin to that which controls the Langlands correspondence, whose geometric meaning is discussed for instance at Weil uniformization and at function field analogy.

References

Revised on August 2, 2017 04:52:20 by David Corfield (91.88.197.172)