Principal series of Hermitian Lie groups induced from Heisenberg parabolic subgroups

Branching of metaplectic representation of 𝑆𝑝(2,ℝ) under its principal 𝕊𝕃(2,ℝ)-subgroup

“…Finally we mention very briefly our motivation, related known results and some perspective questions. Firstly the exact appearance of SL(2, R) ⊂ G = Sp(2, R) and the corresponding branching problem can be used to study the induced representation of the group G 2 from its Heisenberg parabolic subgroup [7]; in [8] we shall study the non-compact realization of induced represenations for Hermitian Lie groups using the related branching of metaplectic representation, the compact picture being studied in [22]. Next this kind of branching problem can be formulated for any real split simple Lie group G. Indeed up to conjugation there is a unique principal subalgebra sl(2, R) (and it might have more than one principal sl(2, R)-subgroups); see [14].…”