Chennai Mathematical Institute


15:00-16:00, Seminar Hall
The restriction of discrete series representations to minimal parabolic subgroups - the case of Spin(4,1)

Aprameyan Parthasarathy
Uni. Paderborn, Germany.


The restriction problem for non-holomorphic discrete series of a real reductive group G to a (minimal) parabolic subgroup P is largely unknown, despite some effort in the previous decades. As a first example in the non-Hermitian case, we study Spin(4,1) - an example that is interesting in itself, and as also serves as a test case for our general strategy. Motivated by geometric considerations we show that only finitely many discrete series of P appear with non-zero multiplicity in the restriction, in contrast to the Hermitian case. Our work is related to certain conjectures of Duflo about the geometric nature of the Plancherel theorem. This is joint work with Gang Liu (Uni. Metz, France).