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Determination of the intertwining operators for holomorphically induced representations of SU(p,q). (English) Zbl 0632.22010
For holomorphically induced representations X, Y for SU(p,q) with integral highest weights and regular infinitesimal characters, the authors describe Hom(X,Y) in terms of two conditions for the existence of a nonzero \({\mathfrak g}\)-module homomorphism between a generalized Verma module and the appropriate generalized Verma module corresponding to the holomorphically induced representation.
Reviewer: R.Fabec
MSC:
22E46 Semisimple Lie groups and their representations
22E47 Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.)
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
17B20 Simple, semisimple, reductive (super)algebras
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References:
[1] Boe, B.D., Collingwood, D.H.: Intertwining operators between holomorphically induced modules. Pac. J. Math. (to appear) · Zbl 0632.22011
[2] Enright, T.J., Shelton, B.: Categories of highest weight modules: applications to classical Hermitian symmetric pairs. Preprint · Zbl 0621.17004
[3] Lascoux, A., Sch?tzenberger, M.-P.: Polyn?mes de Kazhdan et Lusztig pour les grassmanniennes. Ast?risque87-88, 249-266 (1981) · Zbl 0504.20007
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