Affine Grassmannian

In mathematics, the affine Grassmannian of an algebraic group G over a field k is an ind-scheme—a colimit of finite-dimensional schemes—which can be thought of as a flag variety for the loop group G(k((t))) and which describes the representation theory of the Langlands dual group LG through what is known as the geometric Satake correspondence.

For the variety of all k-dimensional affine subspaces of a finite-dimensional vector space (a smooth finite-dimensional variety over k), see affine Grassmannian (manifold).
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