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Component Groups of Centralizers of Nilpotents in Complex Symmetric Spaces

✍ Scribed by Donald R King; Alfred G Noel

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 256 KB
Volume: 232
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8389

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✦ Synopsis

Let G be the adjoint group of a simple Lie algebra , and let K C → Aut C be the complexified isotropy representation at the identity coset of the corresponding symmetric space. If e ∈ C is nilpotent, we consider the centralizer of e in K C . We show that the conjugacy classes of the component group of this centralizer can be described in terms generalizing the Bala-Carter classification of nilpotent orbits in the complexification of .

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