Please use this identifier to cite or link to this item: https://scholarbank.nus.edu.sg/handle/10635/162745
Title: INVARIANTS OF CERTAIN SMOOTH REPRESENTATIONS OF SYMPLECTIC GROUPS
Authors: LI NING
Keywords: degenerate principal series, associated cycles, wave front cycles, the space of generalized Whittaker models, Kostant-Sekiguchi correspondence
Issue Date: 2-Aug-2019
Citation: LI NING (2019-08-02). INVARIANTS OF CERTAIN SMOOTH REPRESENTATIONS OF SYMPLECTIC GROUPS. ScholarBank@NUS Repository.
Abstract: This thesis mainly concerns two topics about certain degenerate principal series representations of symplectic groups. In the first part, we review the theory of associated cycles and wavefront cycles attached to smooth representations of real reductive groups. These two invariants are related to each other via Kostant-Sekiguchi correspondence, and the coefficients of the nilpotent orbits appearing in these cycles are closely related to the dimension of the space of generalized Whittaker models. We compute these two invariants of certain irreducible constituents of degenerate principal series representations of Sp(2n,R) using local theta correspondence. In addition, we show the coefficients of nilpotent orbits of wavefront cycles are the same with the dimension of the space of generalized Whittaker models associated to the nilpotent orbits. In the second part, we prove certain compatibility result between local theta correspondence and the transfer functor. More precisely, we show that the transfer of theta lift of trivial representation of O(m) to Sp(2n,R) is isomorphic to certain constituent of the theta lift of trivial representation of O(p,q) to Sp(2n,R) with p+q=m>n, which extends Jiajun Ma's result to the non stable range case.
URI: https://scholarbank.nus.edu.sg/handle/10635/162745
Appears in Collections:Ph.D Theses (Open)

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