Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups.

DOI10.1134/S0001434609070074zbMath1182.20041arXiv0904.2841MaRDI QIDQ736206

Mikhail V. Ignatyev

Publication date: 27 October 2009

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0904.2841

zbMATH Keywords

Weyl groupsunipotent groupsirreducible complex characterscoadjoint orbitsirreducible representationsroot systemsclassical groups over finite fieldsdimensions of orbitspolarizations of linear forms

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Representation theory for linear algebraic groups (20G05) Root systems (17B22)

Related Items (9)

Tangent cones to Schubert varieties in types \(A_{n}\), \(B_{n}\) and \(C_{n}\) ⋮ Combinatorics of \(B\)-orbits and Bruhat-Chevalley order on involutions. ⋮ Infinite Kostant cascades and centrally generated primitive ideals of \(U(\mathfrak{n})\) in types \(A_\infty\), \(C_\infty\) ⋮ On Involutions in the Weyl Group and B-Orbit Closures in the Orthogonal Case ⋮ Gradedness of the set of rook placements in \(A_{n -1}\) ⋮ On cones tangent to Schubert varieties of type $D_n$ ⋮ The Bruhat-Chevalley order on involutions of the hyperoctahedral group and the combinatorics of \(B\)-orbit closures. ⋮ Centrally generated primitive ideals of \(U(\mathfrak{n})\) in types B and D ⋮ Orthogonal subsets of root systems and the orbit method

Cites Work

• Super-characters of finite unipotent groups of types \(B_n\), \(C_n\) and \(D_n\).
• Representations of finite Chevalley groups. A survey
• Proof of Springer's hypothesis
• Basic sums of coadjoint orbits of the unitriangular group

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