Long Abelian ideals
Copyright policy )Long Abelian ideals
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.
LaTeX2e, 8 pages
- Independent University of Moscow Russian Federation
Mathematics(all), Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Group actions on varieties or schemes (quotients), abelian ideal, Abelian ideal, Borel subalgebra, FOS: Mathematics, Mathematics - Combinatorics, fundamental alcove, Combinatorics (math.CO), Representation Theory (math.RT), Universal enveloping (super)algebras, Fundamental alcove, Mathematics - Representation Theory
Mathematics(all), Representations of Lie algebras and Lie superalgebras, algebraic theory (weights), Group actions on varieties or schemes (quotients), abelian ideal, Abelian ideal, Borel subalgebra, FOS: Mathematics, Mathematics - Combinatorics, fundamental alcove, Combinatorics (math.CO), Representation Theory (math.RT), Universal enveloping (super)algebras, Fundamental alcove, Mathematics - Representation Theory
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