ON INVOLUTIONS OF THE SYMMETRIC GROUP AND CONGRUENCE B-ORBITS OF ANTI-SYMMETRIC MATRICES
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Publication:3094341
DOI10.1142/S0218196711006546zbMath1320.06001arXiv0910.4743OpenAlexW2963030863MaRDI QIDQ3094341
Publication date: 24 October 2011
Published in: International Journal of Algebra and Computation (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0910.4743
anti-symmetric matricescongruence \(B\)-orbitsinvolutions of symmetric groupsposets of matrix varieties
Combinatorics of partially ordered sets (06A07) Algebraic systems of matrices (15A30) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Symmetric groups (20B30)
Related Items (12)
$DIII$ clan combinatorics for the orthogonal Grassmannian ⋮ On the orbits of a Borel subgroup in abelian ideals ⋮ Lexicographic shellability of partial involutions ⋮ Congruence \(B\)-orbits and the Bruhat poset of involutions of the symmetric group ⋮ Bruhat order on partial fixed point free involutions. ⋮ A geometric interpretation of the intertwining number ⋮ Gröbner geometry for skew-symmetric matrix Schubert varieties ⋮ Gröbner geometry for skew-symmetric matrix Schubert varieties ⋮ Monoid embeddings of symmetric varieties ⋮ Universal graph Schubert varieties ⋮ \(K\)-theory formulas for orthogonal and symplectic orbit closures ⋮ Lexicographic shellability of the Bruhat-Chevalley order on fixed-point-free involutions
Cites Work
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- Description of \(\mathbf B\)-orbit closures of order 2 in upper-triangular matrices
- Analogue of the Bruhat decomposition for algebraic monoids
- The Bruhat order on the involutions of the symmetric group
- Linear algebraic monoids.
- Combinatorics of Coxeter Groups
- Steinberg lattice of the general linear group and its modular reduction
- The combinatorics of twisted involutions in Coxeter groups
- A statistic on involutions
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