Long Abelian ideals

Details Long Abelian ideals Long Abelian ideals

2003-03-18

arxiv.org/abs/math/0303222v1

Adv. in Math. 186 (2004), 307-316

Mathematics

Representation Theory

LaTeX2e, 8 pages

Scientific paper

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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