Geometric Langlands duality and representations of algebraic groups over commutative rings

Details Geometric Langlands duality and representations of algebraic groups over commutative rings Geometric Langlands duality and representations of algebraic groups over commutative rings

2004-01-18

arxiv.org/abs/math/0401222v4

Mathematics

Representation Theory

Scientific paper

In this paper we give a geometric version of the Satake isomorphism. Given a connected complex reductive algebraic group, we show that the category of representations of its Langlands dual is naturally equivalent to a certain category of perverse sheaves on the complex affine Grassmannian. We can work with perverse sheaves with coefficients in an arbitrary commutative ring and then we recover the representation theory of the split form of the dual group over the commutative ring.

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