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Symmetric pairs and associated commuting varieties

Published online by Cambridge University Press:  01 September 2007

DMITRI PANYUSHEV  and
OKSANA YAKIMOVA
DMITRI PANYUSHEV
Affiliation:
Independent University of Moscow, Bol'shoi Vlasevskii per. 11, 119002 Moscow, Russia. email: [email protected]
OKSANA YAKIMOVA
Affiliation:
MPI für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany. email: [email protected]
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Abstract

Let be a -grading of a simple Lie algebra . The commuting variety associated with such a grading is the variety of pairs of commuting elements from . We study the problem of irreducibility of these varieties. Using invariant-theoretic technique, we present new instances of reducible and irreducible commuting varieties.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 2 , September 2007 , pp. 307 - 321
Copyright
Copyright © Cambridge Philosophical Society 2007

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