Lusztig correspondence and Howe correspondence on cuspidal characters
Shu-Yen Pan ( National Tsing Hua University )
2016-09-23 13:30 - 14:30
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)
Let (G,G') be a finite reductive dual pair of a symplectic group and an orthogonal group. The Howe correspondence establishes a correspondence between a subset of irreducible characters of G and a subset of irreducible characters of G'. On the other hand, the set of irreducible characters of G partitions into subsets (called Lusztig series) indexed by conjugacy classes (s) of semisimple elements in the dual group of G. The Lusztig correspondence is a bijection between the Lusztig series indexed by (s) and the set of irreducible unipotent characters of the centralizer of s in the dual group of G. In this talk, I would like to discuss the compatibility between these two correspondences on cuspidal characters.