scientific article

zbMath0870.20047MaRDI QIDQ3123640

Louis Solomon

Publication date: 22 July 1997

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

weightsrootsHecke algebrasWeyl groupsidempotentsparabolic subgroupslinear algebraic groupsreductive algebraic groupsfinite groups of Lie typegroups of unitsFrobenius mapsBorel subgroupsTits buildingsmaximal torifinite reductive groupslinear algebraic monoidsreductive monoidsRenner monoidsBruhat decompositionsfinite reductive monoids\(BN\)-pairsfinite monoids of Lie typePutcha cross section latticestotal matrix monoidsZariski closed submonoids

Mathematics Subject Classification ID

Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Linear algebraic groups over arbitrary fields (20G15) Linear algebraic groups over finite fields (20G40) Semigroups of transformations, relations, partitions, etc. (20M20) Group actions on varieties or schemes (quotients) (14L30) Regular semigroups (20M17) Other geometric groups, including crystallographic groups (20H15) Groups with a (BN)-pair; buildings (20E42) Inverse semigroups (20M18) Research exposition (monographs, survey articles) pertaining to group theory (20-02)

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A generic algebra associated to certain Hecke algebras. ⋮ Betti Numbers of Toric Varieties and Eulerian Polynomials ⋮ Descent systems for Bruhat posets ⋮ Big cells and LU factorization in reductive monoids ⋮ The lattice of \(\mathcal J\)-classes of \(({\mathcal J},\sigma)\)-irreducible monoids ⋮ Polynomial representations, algebraic monoids, and Schur algebras of classical type ⋮ Infinite-dimensional reductive monoids associated to highest weight representations of Kac-Moody groups ⋮ Algebraic Monoids and Renner Monoids ⋮ Conjugacy Decomposition of Canonical and Dual Canonical Monoids ⋮ Irreducible representations of semisimple algebraic groups and supersolvable lattices. ⋮ 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. ⋮ Generic Hecke algebra for Renner monoids. ⋮ Equivariant cohomology of rationally smooth group embeddings ⋮ The \(H\)-polynomial of a semisimple monoid. ⋮ Shellability in reductive monoids ⋮ Subspace semigroups ⋮ Stable reductive varieties. I: Affine varieties ⋮ Partial symmetry, reflection monoids and Coxeter groups. ⋮ Factorizable inverse monoids. ⋮ Orders of the Renner monoids. ⋮ Enumeration of symplectic and orthogonal injective partial transformations. ⋮ The sympathetic sceptic's guide to semigroup representations ⋮ Characters of Renner monoids and their Hecke algebras ⋮ On \(\mathbb{P} M\)-monoids and braid \(\mathbb{P} M\)-monoids ⋮ Types of reductive monoids ⋮ The lattice of \(\mathcal J\)-classes of \(({\mathcal J},\sigma)\)-irreducible monoids. II ⋮ The ring of regular functions of an algebraic monoid ⋮ Möbius function on cross-section lattices. ⋮ The rook monoid is lexicographically shellable ⋮ The Orbit Structures of (, σ)-Irreducible Monoids ⋮ Maximal subgroups of free idempotent generated semigroups over the full linear monoid

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