The aim of this paper is to identify a certain tensor category of perverse sheaves on the loop Grassmannian Gr(R) of a real form G(R) of a connected reductive complex algebraic group G with the category of finite-dimensional representations of a connected reductive complex algebraic subgroup H of the dual group. G. The root system of H is closely related to the restricted root system of G(R). The fact that 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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机译：本文的目的是在连通的还原复代数群G的实型G（R）的环Grassmannian Gr（R）上确定逆滑轮的某个张量类别，该类别具有连通的有限维表示形式对偶组的归约复数子集H。 G. H的根系与G（R）的受限根系密切相关。 H是可归约的事实意味着一个有趣的实数代数映射族满足Beilinson-Bernstein-Deligne分解定理的结论。
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