Mathematics – Representation Theory
Scientific paper
2003-03-18
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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