Ad-nilpotent ideals of a Borel subalgebra. II.

DOI10.1016/S0021-8693(02)00532-XzbMath1033.17008arXivmath/0106057OpenAlexW2137493405MaRDI QIDQ1858271

Paolo Papi, Paola Cellini

Publication date: 12 February 2003

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0106057

zbMATH Keywords

Coxeter numbercoroot lattice

Mathematics Subject Classification ID

Structure theory for Lie algebras and superalgebras (17B05)

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Normalizers of ad-nilpotent ideals, Long Abelian ideals, Abelian ideals of Borel subalgebras and affine Weyl groups, ad-nilpotent ideals of a Borel subalgebra: generators and duality, Dominant regions in noncrystallographic hyperplane arrangements, Combinatorial analogues of ad-nilpotent ideals for untwisted affine Lie algebras, Weight posets associated with gradings of simple Lie algebras, Weyl groups, and arrangements of hyperplanes, The Catalan combinatorics of the hereditary artin algebras, Constructing characters of Sylow \(p\)-subgroups of finite Chevalley groups, Decomposition rules for conformal pairs associated to symmetric spaces and Abelian subalgebras of \(\mathbb Z_{2}\)-graded Lie algebras, On a refinement of the generalized Catalan numbers for Weyl groups, Evidence for parking conjectures, Ad-nilpotent ideals and the Shi arrangement, Rational associahedra and noncrossing partitions, Antichains in weight posets associated with gradings of simple Lie algebras, Oriented tree diagram Lie algebras and their abelian ideals, On the characters of the Sylow -subgroups of untwisted Chevalley groups, Labeling the regions of the type \(C_n\) Shi arrangement, Promotion and rowmotion, Short antichains in root systems, semi-Catalan arrangements, and \(B\)-stable subspaces., Parking spaces., NILPOTENT SUBSPACES AND NILPOTENT ORBITS, A transitivity result for ad-nilpotent ideals in type \(A\), Ad-nilpotent ideals of a parabolic subalgebra, Ad-nilpotent ideals and equivalence relations, Abelian ideals of a Borel subalgebra and root systems, The poset of positive roots and its relatives, On orbits of antichains of positive roots, Non-linear maps preserving ideals on a parabolic subalgebra of a simple algebra, Nonlinear Maps on a Borel Subalgebra Preserving Ad-Nilpotent Ideals, Abelian ideals of a Borel subalgebra and subsets of the Dynkin diagram, Generalized noncrossing partitions and combinatorics of Coxeter groups, A uniform bijection between nonnesting and noncrossing partitions, Abelian Ideals with Given Dimension in Borel Subalgebras, Symmetry of Narayana Numbers and Rowvacuation of Root Posets, Arrangements of ideal type

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