Seminars

Lusztig correspondence and Howe correspondence on cuspidal characters

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Seminars

Shu-Yen Pan

2016-09-23
13:30:00 - 14:30:00

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.