Unipotent representations and the dual pair correspondence

2016/09/28 by Barbasch, Dan
#22E46 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1609.08998

Abstract

This paper provides a construction of the unipotent representations for classical complex groups in terms of the Theta correspondence as introduced and studied by R. Howe. The K-type structure of unipotent representations is obtained as a consequence of the character formulas for unipotent representations of D. Vogan and the author. This provides a tight link between unipotent representations and the orbit philosophy. A parametrization of unipotent representations for the Spin groups is obtained.

Related

• Unipotent Ideals for Spin and Exceptional Groups
• A parametrization of unipotent representations
• Unipotent Representations Attached to the Principal Nilpotent Orbit
• Theta correspondence and Springer correspondence
• Special unipotent representations of real classical groups: construction and unitarity