Gradedness of the set of rook placements in \(A_{n -1}\)

DOI10.2478/cm-2021-0016OpenAlexW3200558739MaRDI QIDQ2245601

Mikhail V. Ignatyev

Publication date: 15 November 2021

Published in: Communications in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.01673

zbMATH Keywords

coadjoint orbitroot systemgraded posetBorel subgrouprook placement

Mathematics Subject Classification ID

Combinatorics of partially ordered sets (06A07) Root systems (17B22) Coadjoint orbits; nilpotent varieties (17B08)

Cites Work

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• Orthogonal subsets of classical root systems and coadjoint orbits of unipotent groups.
• The Bruhat-Chevalley order on involutions of the hyperoctahedral group and the combinatorics of \(B\)-orbit closures.
• Super-characters of finite unipotent groups of types \(B_n\), \(C_n\) and \(D_n\).
• Description of \(\mathbf B\)-orbit closures of order 2 in upper-triangular matrices
• The Bruhat order on the involutions of the symmetric group
• Combinatorics of \(B\)-orbits and Bruhat-Chevalley order on involutions.
• Rooks on Ferrers boards and matrix integrals
• \(B\)-orbits in solutions to the equation \(X^2=0\) in triangular matrices
• Involutions in \(S_n\) and associated coadjoint orbits
• Orthogonal subsets of root systems and the orbit method
• UNITARY REPRESENTATIONS OF NILPOTENT LIE GROUPS
• Rook placements in $A_n$ and combinatorics of $B$-orbit closures
• The basic character table of the unitriangular group

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