Heisenberg parabolically induced representations of Hermitian Lie groups, Part I: Intertwining operators and Weyl transform

Principal series of Hermitian Lie groups induced from Heisenberg parabolic subgroups

“…In a forthcoming work [6] we shall study the maximal parabolically induced representations for the group G 2 ; there are two families of maximal parabolic subgroups one of which is Heisenberg. This case is somewhat different from the rank four cases.…”

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].…”