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On unipotent representations of real classical groups
马家骏 研究员(上海交通大学)
05月24日(周四)下午 13:00—14:30  华东师范大学闵行校区数学系126室

摘要: In this talk, I will present a recent work with Binyong Sun and Chengbo Zhu on unipotent representations of real classical groups (real symplectic groups, real orthogonal groups, quaternionic orthogonal groups or quaternionic symplectic groups). Unipotent representations are certain irreducible admissible representations characterized by their associated varieties and infinitesimal character. They consist the unipotent L-packet in Langlands' philosophy and they are related to the quantization of nilpotent orbits. In Barbasch and Vogan established the theory of special unipotent representations for complex classical groups and unitary groups. They also made conjectures for the general case, including a conjecture that unipotent representations attached to special nilpotent orbits should be unitarizable. In 90's, thanks to many peoples work, it becomes clear that iterated theta lifting could be an effective way to construct unipotent representations of real classical groups. In our work, we solved the unitarity problem for rigid special unipotent oribts utilizing algebraic and analytical properties of theta lifts. Along the proof we also established some other properties of these representations.