Abelian ideals of a Borel subalgebra and root systems

DOI10.4171/JEMS/496zbMath1362.17013arXiv1205.5983OpenAlexW2963584737MaRDI QIDQ2256066

Dmitri I. Panyushev

Publication date: 19 February 2015

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.5983

zbMATH Keywords

minuscule elementroot systemBorel subalgebraabelian ideal

Mathematics Subject Classification ID

Reflection and Coxeter groups (group-theoretic aspects) (20F55) Simple, semisimple, reductive (super)algebras (17B20) Root systems (17B22)

Related Items

On the orbits of a Borel subgroup in abelian ideals, Minimal inversion complete sets and maximal abelian ideals, Abelian ideals of a Borel subalgebra and root systems. II, Abelian ideals and amazing roots, Casimir elements associated with Levi subalgebras of simple Lie algebras and their applications, Glorious pairs of roots and abelian ideals of a Borel subalgebra

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Abelian ideals of a Borel subalgebra and subsets of the Dynkin diagram
• Short antichains in root systems, semi-Catalan arrangements, and \(B\)-stable subspaces.
• Ad-nilpotent ideals of a Borel subalgebra. II.
• Abelian ideals in a Borel subalgebra of a complex simple Lie algebra
• Abelian ideals of Borel subalgebras and affine Weyl groups
• \(ad\)-nilpotent ideals of a Borel subalgebra
• The poset of positive roots and its relatives
• Groupes et algébras de Lie
• Coxeter and dual coxeter numbers
• Orbital varieties of the minimal orbit
• Spherical orbits and Abelian ideals