UNIPOTENT REPRESENTATIONS AND REDUCTIVE DUAL PAIRS OVER FINITE-FIELDS

Consider the representation correspondence for a reductive dual pair (G1 , G2) over a finite field. We consider the question of how the correspondence behaves for unipotent representations. In the special case of cuspidal unipotent representations, and a certain fundamental situation, that of 'first occurrence'', the representation correspondence takes a cuspidal unipotent representation of G1 to one of G2 . This should serve as a fundamental case in studying the correspondence in general over both finite and local fields.