Local theta correspondence of some supercuspidal representations
10:10 - 11:00
101 , Mathematics Research Center Building (ori. New Math. Bldg.)
The preservation principle of the local theta correspondence predicts the existence of a chain of irreducible supercuspidal representations of p-adic classical groups.
In this talk, I want to give an explicit characterization of the chain starting from an irreducible supercuspidal representations of a unitary group of one variable or an orthogonal group of two variables.
In particular, I will define the Lusztig-like correspondence of generic cuspidal data for p-adic groups and establish its relation with local theta correspondence of supercuspidal representations for p-adic dual pairs.