The Bruhat-Chevalley order on involutions of the hyperoctahedral group and the combinatorics of \(B\)-orbit closures.

DOI10.1007/s10958-013-1386-6zbMath1301.20034arXiv1112.2624OpenAlexW2045308384MaRDI QIDQ744485

Mikhail V. Ignatyev

Publication date: 25 September 2014

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1112.2624

zbMATH Keywords

Weyl groupsZariski closuressymplectic groupsroot systemsorbit closuresBorel subgroupsBruhat-Chevalley ordercoadjoint actionsposets of involutions

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representation theory for linear algebraic groups (20G05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Classical groups (algebro-geometric aspects) (14L35) Coadjoint orbits; nilpotent varieties (17B08)

Related Items (7)

Tangent cones to Schubert varieties in types \(A_{n}\), \(B_{n}\) and \(C_{n}\) ⋮ Infinite Kostant cascades and centrally generated primitive ideals of \(U(\mathfrak{n})\) in types \(A_\infty\), \(C_\infty\) ⋮ B-orbits of square zero in nilradical of the symplectic algebra ⋮ 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 $D_n$ ⋮ Nilpotent orbits of height 2 and involutions in the affine Weyl group

Cites Work

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• The Bruhat order on symmetric varieties
• The Bruhat order on the involutions of the hyperoctahedral group.
• Singular loci of Schubert varieties
• The Bruhat order on the involutions of the symmetric group
• \(B\)-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

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