| Popis: |
In this article the author presents the results on the explicit construction of the intertwining operator between a holomorphic discrete series representation of some Lie group G and that of some subgroup G1 G. More precisely, we construct a G1-intertwining projection operator from a representation H of G onto a representation H1 of G1 as a differential operator, in the case (G,G1) = (G0 ×G0,ΔG0) and both H, H1 are of scalar type, and also construct a G1-intertwining embedding operator from H1 of G1 into H of G as an infinite-order differential operator, in the case H is of scalar type and H1 is multiplicity-free under a maximal compact subgroup K1 G1. In this paper we mainly deal with the case (G,G1) = (Sp(1,R)×Sp(1,R),ΔSp(1,R)) and the cases (G,G1) = (SU(s, s), Sp(s,R)), (SU(s, s),SO (2s)). |
