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Long Abelian ideals

Dmitri I. Panyushev
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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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BibTeXRIS

Dmitri I. Panyushev. 2003-03-18. Long Abelian ideals. https://arxiv.org/abs/math/0303222

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