Analogue of the Bruhat decomposition for algebraic monoids

DOI10.1016/0021-8693(86)90197-3zbMath0595.20064OpenAlexW2062464706MaRDI QIDQ1077550

Lex E. Renner

Publication date: 1986

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(86)90197-3

zbMATH Keywords

Weyl groupBruhat decompositionrow reductionTits systemcross-section latticesreductive, algebraic monoids

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) General structure theory for semigroups (20M10) Semigroups of transformations, relations, partitions, etc. (20M20)

Related Items (66)

TRIANGULAR MONOIDS AND AN ANALOG TO THE DERIVED SEQUENCE OF A SOLVABLE GROUP ⋮ The Canonical Compactification of a Finite Group of Lie Type ⋮ R-POLYNOMIALS OF FINITE MONOIDS OF LIE TYPE ⋮ Extending the Bruhat order and the length function from the Weyl group to the Weyl monoid. ⋮ Betti Numbers of Toric Varieties and Eulerian Polynomials ⋮ Cell Decompositions of the Special Orthogonal Algebraic Monoids ⋮ Descent systems for Bruhat posets ⋮ Big cells and LU factorization in reductive monoids ⋮ Poisson structures on affine spaces and flag varieties. I: Matrix affine Poisson space. ⋮ Centralizer of an idempotent in a reductive monoid ⋮ Connected algebraic monoids ⋮ Analogue of the Bruhat-Chevalley order for reductive monoids ⋮ Enumeration of injective partial transformations ⋮ Classification of semisimple varieties ⋮ On embeddings of certain spherical homogeneous spaces in prime characteristic ⋮ Infinite-dimensional reductive monoids associated to highest weight representations of Kac-Moody groups ⋮ Conjugacy classes in the symplectic Renner monoid. ⋮ Asymptotic semigroups and two-sided weak orders ⋮ Lexicographic shellability of partial involutions ⋮ Stirling posets ⋮ Idempotent conjugacy in monoids ⋮ Congruence \(B\)-orbits and the Bruhat poset of involutions of the symmetric group ⋮ Sects ⋮ Algebraic Monoids and Renner Monoids ⋮ Conjugacy Decomposition of Canonical and Dual Canonical Monoids ⋮ On the Borel submonoid of a symplectic monoid ⋮ The Bruhat-Chevalley-Renner order on the set partitions ⋮ The \(H\)-polynomial of an irreducible representation. ⋮ REPRESENTATIONS OF THE SYMPLECTIC ROOK MONOID ⋮ H-POLYNOMIALS AND ROOK POLYNOMIALS ⋮ Idempotent lattices, Renner monoids and cross section lattices of the special orthogonal algebraic monoids. ⋮ The Iwahori algebra of \(\mathbf M_n(\mathbf F_q)\). A presentation and a representation on tensor space. ⋮ Nilpotent variety of a reductive monoid. ⋮ Bruhat order on partial fixed point free involutions. ⋮ A geometric interpretation of the intertwining number ⋮ ROOT SEMIGROUPS IN REDUCTIVE MONOIDS ⋮ Equivariant cohomology of rationally smooth group embeddings ⋮ Monoid Hecke algebras ⋮ The \(H\)-polynomial of a semisimple monoid. ⋮ Möbius functions and semigroup representation theory. II: Character formulas and multiplicities. ⋮ Sandwich Matrices, Solomon Algebras, and Kazhdan-Lusztig Polynomials ⋮ Invariant convex subcones of the Tits cone of a linear Coxeter group ⋮ Shellability in reductive monoids ⋮ Bruhat-Chevalley order in reductive monoids. ⋮ Regular Linear Algebraic Monoids ⋮ THE RENNER MONOIDS AND CELL DECOMPOSITIONS OF THE SYMPLECTIC ALGEBRAIC MONOIDS ⋮ Partial symmetry, reflection monoids and Coxeter groups. ⋮ Möbius functions and semigroup representation theory. ⋮ Orders of the Renner monoids. ⋮ The Maximal Chains of the Extended Bruhat Orders on the  × -Orbits of an Infinite Renner Monoid ⋮ Conjugacy Classes in Algebraic Monoids ⋮ Bruhat-Chevalley order on \(\mathcal J\)-classes of reductive monoids. ⋮ REPRESENTATIONS OF THE RENNER MONOID ⋮ Monoid embeddings of symmetric varieties ⋮ ON INVOLUTIONS OF THE SYMMETRIC GROUP AND CONGRUENCE B-ORBITS OF ANTI-SYMMETRIC MATRICES ⋮ Monoids on groups with BN-pairs ⋮ Canonical Cellular Decomposition for 𝒥-Irreducible Monoids ⋮ The rook monoid is lexicographically shellable ⋮ The Symplectic Monoid ⋮ Monoid deformations and group representations ⋮ The Orbit Structures of (, σ)-Irreducible Monoids ⋮ Weak order on complete quadrics ⋮ Conjugacy decomposition of reductive monoids. ⋮ The centraliser of a semisimple element on a reductive algebraic monoid ⋮ PARABOLIC MONOIDS I: STRUCTURE ⋮ FINE BRUHAT INTERSECTIONS FOR REDUCTIVE MONOIDS

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