Intertwining operators between holomorphically induced modules
type: Item
instance of: scholarly article
title: Intertwining operators between holomorphically induced modules
zbMATH Open document ID: 0632.22011
author: Brian D. Boe
author: David H. Collingwood
published in: Pacific Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The authors investigate the existence of covariant differential intertwining operators for members in the family of continued holomorphic discrete series for the groups SU(p,q), Sp(n,\({\mathbb{R}})\), \(SO^*(2n)\) and for the exceptional cases \(E_ 6\) and \(E_ 7\). These spaces of intertwining operators are isomorphic to the space of \({\mathfrak g}\)- homomorphisms between generalized Verma modules corresponding to regular integrals. The authors show these spaces are at most one-dimensional and can be computed algorithmically from lower-dimensional cases. For \(E_ 6\) and \(E_ 7\) a brief description of the homomorphisms is made modulo the homomorphisms between certain simpler singular modules.
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 22E47
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B20
zbMATH DE Number: 4027781
zbMATH Keywords: hermitian symmetric pair
zbMATH Keywords: holomorphically induced representations
zbMATH Keywords: intertwining operators
zbMATH Keywords: holomorphic discrete series
zbMATH Keywords: generalized Verma modules
zbMATH Keywords: regular integrals
MaRDI profile type: Publication
full work available at URL: pjm.1986.124.73
OpenAlex ID: W1977288397
DOI: 10.2140/PJM.1986.124.73
description: scientific article; zbMATH DE number 4027781