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Perverse sheaves on real loop Grassmannians

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Abstract

The aim of this paper is to identify a certain tensor category of perverse sheaves on the loop Grassmannian Grℝ of a real form Gℝ of a connected reductive complex algebraic group G with the category of finite-dimensional representations of a connected reductive complex algebraic subgroup \(\check{H}\) of the dual group \(\check{G}\). The root system of \(\check{H}\) is closely related to the restricted root system of Gℝ. The fact that \(\check{H}\) is reductive implies that an interesting family of real algebraic maps satisfies the conclusion of the Decomposition Theorem of Beilinson-Bernstein-Deligne.

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  1. Department of Mathematics, University of Chicago, Chicago, IL, 60637, USA

    David Nadler

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  1. David Nadler
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Correspondence to David Nadler.

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Nadler, D. Perverse sheaves on real loop Grassmannians. Invent. math. 159, 1–73 (2005). https://doi.org/10.1007/s00222-004-0382-3

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