Shellability in reductive monoids

DOI10.1090/S0002-9947-01-02806-9zbMath0988.20055OpenAlexW1563433788MaRDI QIDQ2750959

Putcha, Mohan S.

Publication date: 21 October 2001

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-01-02806-9

zbMATH Keywords

Weyl groupsorbitspartially ordered setsunit groupsBorel subgroupsreductive monoidsRenner monoidsretractsshellability of Bruhat-Chevalley orders on Weyl groups

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Semigroups of transformations, relations, partitions, etc. (20M20) Combinatorics of partially ordered sets (06A07)

Related Items

R-POLYNOMIALS OF FINITE MONOIDS OF LIE TYPE ⋮ Extending the Bruhat order and the length function from the Weyl group to the Weyl monoid. ⋮ Big cells and LU factorization in reductive monoids ⋮ Lexicographic shellability of partial involutions ⋮ Conjugacy Decomposition of Canonical and Dual Canonical Monoids ⋮ Irreducible representations of semisimple algebraic groups and supersolvable lattices. ⋮ H-POLYNOMIALS AND ROOK POLYNOMIALS ⋮ Nilpotent variety of a reductive monoid. ⋮ Bruhat order on partial fixed point free involutions. ⋮ ROOT SEMIGROUPS IN REDUCTIVE MONOIDS ⋮ Bruhat-Chevalley order in reductive monoids. ⋮ The Maximal Chains of the Extended Bruhat Orders on the  × -Orbits of an Infinite Renner Monoid ⋮ Bruhat-Chevalley order on \(\mathcal J\)-classes of reductive monoids. ⋮ The rook monoid is lexicographically shellable ⋮ Weak order on complete quadrics ⋮ Conjugacy decomposition of reductive monoids. ⋮ PARABOLIC MONOIDS I: STRUCTURE ⋮ Lexicographic shellability of the Bruhat-Chevalley order on fixed-point-free involutions

Cites Work

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• The Bruhat decomposition, Tits system and Iwahori ring for the monoid of matrices over a finite field
• A semigroup approach to linear algebraic groups
• On some geometric aspects of Bruhat orderings. I: A finer decomposition of Bruhat cells
• Analogue of the Bruhat decomposition for algebraic monoids
• The system of idempotents and the lattice of \({\mathcal J}\)-classes of reductive algebraic monoids
• Bruhat order of Coxeter groups and shellability
• Classical Bruhat orders and lexicographic shellability
• Analogue of the Bruhat-Chevalley order for reductive monoids
• Polynomial representations, algebraic monoids, and Schur algebras of classical type
• Shellings of spheres and polytopes
• Analogue of the Bruhat decomposition for algebraic monoids. II: The length function and the trichotomy
• Combinatorics and commutative algebra.
• Introduction to Toric Varieties. (AM-131)
• Shellable and Cohen-Macaulay Partially Ordered Sets
• Arithmetic Cohen-Macaulayness and Arithmetic Normality for Schubert Varieties