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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hermitian Lie algebras and metaplectic representations. I


Authors: Shlomo Sternberg and Joseph A. Wolf
Journal: Trans. Amer. Math. Soc. 238 (1978), 1-43
MSC: Primary 22E45; Secondary 32M15, 81.22
MathSciNet review: 0486325
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Abstract: A notion of ``hermitian Lie algebra'' is introduced which relates ordinary and graded Lie algebra structures. In the case of real-symplectic and arbitrary-signature-unitary Lie algebras, it leads to an analysis of the minimal dimensional coadjoint orbits, and then to the metaplectic representations and their restrictions to unitary groups of arbitrary signature and parabolic subgroups of these unitary groups.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1978-0486325-5
PII: S 0002-9947(1978)0486325-5
Article copyright: © Copyright 1978 American Mathematical Society