Spherical Orbits and Abelian Ideals

By Dmitri I. Panyushev, G. Röhrle. 2001

47 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/75af2850f107dd141aedf0c9d0d6332cf58a747a

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In Algebra and Number Theory

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In Geometry and Topology

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In Mathematical Physics

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Citations in the corpus

• Ad-nilpotent ideals of a Borel subalgebra II (2001, unknown): “The abelian ideals of Borel subalgebras were studied by Kostant in [Ko1], [Ko2] in connection with representation theory of compact semisimple Lie groups, and very recently by Panyushev and R¨ohr le , [PR], in connection with the theory of spherical orbits.”
• Abelian ideals in a Borel subalgebra of a complex simple Lie algebra (2002, background): “ This will then extend and give an a priori explanation for the observation that the maximal abelian ideals are in canonical one-toone correspondence with the simple long roots, as it was recorded in [PR]. We need some preparation. Recall that the height ht(ϕ) of a root ϕ= Pl i=1 ciαiis defined to be”