标题： 内窥镜对有限域上不连通半单群的表示 显示英文标题

标题： Endoscopy for representations of disconnected reductive groups over finite fields

摘要： 设G为有限域上连通半单群的有理点群。 基于Lusztig和Yun的工作，我们使不可约G表示的Jordan分解成为规范的。 其形式为具有固定半单参数s的G表示范畴与G的一个内窥群的拟幂零表示范畴之间的等价关系，该等价关系以s的中心化子的成分群上的同变结构进行丰富。 接下来我们推广这些结果，将连通半单群替换为具有半单中性成分的光滑群概形。 同样地，我们根据内窥群的拟幂零表示，建立了G表示的有理系列和几何系列之间的规范等价关系。 显示英文摘要

摘要： Let G be the group of rational points of a connected reductive group over a finite field. Based on work of Lusztig and Yun, we make the Jordan decomposition for irreducible G-representations canonical. It comes in the form of an equivalence between the category of G-representations with a fixed semisimple parameter s and the category of unipotent representations of an endoscopic group of G, enriched with an equivariant structure with respect to the component group of the centralizer of s. Next we generalize these results, replacing the connected reductive group by a smooth group scheme with reductive neutral component. Again we establish canonical equivalences for both the rational and the geometric series of G-representations, in terms of unipotent representations of endoscopic groups.