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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Homomorphisms between generalized Verma modules


Author: Brian D. Boe
Journal: Trans. Amer. Math. Soc. 288 (1985), 791-799
MSC: Primary 17B10
DOI: https://doi.org/10.1090/S0002-9947-1985-0776404-0
MathSciNet review: 776404
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Abstract: Let $ \mathfrak{g}$ be a finite-dimensional complex semisimple Lie algebra and $ \mathfrak{p}$ a parabolic subalgebra. The first result is a necessary and sufficient condition, in the spirit of the Bernstein-Gelfand-Gelfand theorem on Verma modules, for Lepowsky's "standard map" between two generalized Verma modules for $ \mathfrak{g}$ to be zero. The main result gives a complete description of all homomorphisms between the generalized Verma modules induced from one-dimensional $ \mathfrak{p}$-modules, in the "hermitian symmetric" situation.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1985-0776404-0
Keywords: Generalized Verma module, homomorphism, standard map, hermitian symmetric space, semi-invariant
Article copyright: © Copyright 1985 American Mathematical Society