|Finite Theta Correspondence, Unipotent Support and Orbit Correspondence
|For a finite reductive dual pair of a symplectic group and an orthogonal group, the theta correspondence establishes an important relation between the irreducible representations of these two groups. On the other hand, we also have the orbit correspondence between the unipotent classes of these two groups. In this talk, we would like to discuss a nice relation between these two correspondences. More precisely, we show that if two irreducible representations are paired by the theta correspondence, then the unipotent supports of their Alvis-Curtis duals are paired by the orbit correspondence.