Long Abelian ideals |
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Authors: | Dmitri I. Panyushev |
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Affiliation: | Independent University of Moscow, Bol'shoi Vlasevskii per. 11, 121002 Moscow, Russia |
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Abstract: | We study Abelian ideals of a Borel subalgebra consisting of long roots. It is shown that methods of Cellini and Papi can be extended to this situation. A uniform expression for the number of long Abelian ideals is given. We also show that there is a one-to-one correspondence between the long Abelian ideals and B-stable commutative subalgebras in the little adjoint representation of the Langlands dual Lie algebra. |
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Keywords: | 14L30 17B10 17B35 |
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