Journal of the Mathematical Society of Japan

Isotropy subalgebras of elliptic orbits in semisimple Lie algebras, and the canonical representatives of pseudo-Hermitian symmetric elliptic orbits

Nobutaka BOUMUKI

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We give a method of determining the centralizer of an elliptic element in a real semisimple Lie algebra g , in relation with the maximal compact subalgebra of g and the compact dual of g . Moreover, we determine a special central element (called the H -element) of the isotropy subalgebra of each simple irreducible pseudo-Hermitian symmetric Lie algebra.

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J. Math. Soc. Japan, Volume 59, Number 4 (2007), 1135-1177.

First available in Project Euclid: 10 December 2007

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Primary: 17B20: Simple, semisimple, reductive (super)algebras
Secondary: 53C35: Symmetric spaces [See also 32M15, 57T15]

real semisimple Lie algebra elliptic element centralizer duality pseudo-Hermitian symmetric Lie algebra


BOUMUKI, Nobutaka. Isotropy subalgebras of elliptic orbits in semisimple Lie algebras, and the canonical representatives of pseudo-Hermitian symmetric elliptic orbits. J. Math. Soc. Japan 59 (2007), no. 4, 1135--1177. doi:10.2969/jmsj/05941135.

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