Ad-nilpotent ideals and the Shi arrangement
نویسندگان
چکیده
منابع مشابه
Normalizers of ad-nilpotent ideals
Let g be a complex simple Lie algebra. Fix a Borel subalgebra b and a Cartan subalgebra t ⊂ b. The nilpotent radical of b is denoted by u. The corresponding set of positive (resp. simple) roots is ∆ (resp. Π). An ideal of b is called ad-nilpotent, if it is contained in [b, b]. The theory of ad-nilpotent ideals has attracted much recent attention in the work of Kostant, Cellini-Papi, Sommers, an...
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This paper is about two arrangements of hyperplanes. The first — the Shi arrangement — was introduced by Jian-Yi Shi to describe the Kazhdan-Lusztig cells in the affine Weyl group of type A. The second — the Ish arrangement — was recently defined by the first author who used the two arrangements together to give a new interpretation of the q, t-Catalan numbers of Garsia and Haiman. In the prese...
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We provide explicit formulas for the number of ad-nilpotent ideals of a Borel subalgebra of a complex simple Lie algebra having fixed class of nilpotence.
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This paper is devoted to a detailed study of certain remarkable posets which form a natural partition of all abelian ideals of a Borel subalgebra. Our main result is a nice uniform formula for the dimension of maximal ideals in these posets. We also obtain results on ad-nilpotent ideals which complete the analysis started in [CP2], [CP3].
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2013
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2013.08.004