Hermitian Lie algebras and metaplectic representations. I

Sternberg, Shlomo; Wolf, Joseph A.

doi:10.1090/S0002-9947-1978-0486325-5

Hermitian Lie algebras and metaplectic representations. I
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by Shlomo Sternberg and Joseph A. Wolf PDF

Trans. Amer. Math. Soc. 238 (1978), 1-43 Request permission

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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