Intertwining operators between holomorphically induced modules

Brian Boe and David H. Collingwood

Vol. 124 (1986), No. 1, 73–84

DOI: 10.2140/pjm.1986.124.73

Abstract

Let (G,K) be an irreducible hermitian symmetric pair of non-compact type. The authors study the spaces of covariant differential intertwining operators between the continuations of holomorphic discrete series for this pair. In particular, when G = SU(p,q), Sp(n,R), or SO^∗(2n), an algorithm is provided to reduce the problem for regular integral infinitesimal character to that for semiregular representations. In case G = SU(p,q), this latter problem is solved using an equivalence of categories due to Enright-Shelton (providing a reduction to the regular case for a lower rank group).

In addition, an explicit description of the non-zero spaces of intertwining operators is given for the two exceptional cases, E₆ and E₇. The remaining case, G = SO(2,n), has been treated previously. All results are obtained in the (dual) setting of homomorphisms between generalized Verma modules.

Mathematical Subject Classification 2000

Primary: 22E47

Milestones

Received: 2 April 1985

Published: 1 September 1986