The Betti Numbers of Simple Embeddings

DOI10.1007/978-1-4939-0938-4_11zbMath1434.14021OpenAlexW1016352591MaRDI QIDQ5112363

Lex E. Renner

Publication date: 29 May 2020

Published in: Algebraic Monoids, Group Embeddings, and Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4939-0938-4_11

zbMATH Keywords

Betti numbersdescent systemsrationally smoothH-polynomials

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Group actions on varieties or schemes (quotients) (14L30) Compactifications; symmetric and spherical varieties (14M27) Algebraic monoids (20M32)

Cites Work

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• Weyl groups, descent systems and Betti numbers.
• The \(H\)-polynomial of an irreducible representation.
• Descent systems for Bruhat posets
• The system of idempotents and the lattice of \({\mathcal J}\)-classes of reductive algebraic monoids
• The behavior at infinity of the Bruhat decomposition
• Singular loci of Schubert varieties
• Intersection cohomology of reductive varieties
• Linear algebraic monoids.
• Some theorems on actions of algebraic groups
• Bruhat lattices, plane partition generating functions, and minuscule representations
• Rationally smooth algebraic monoids.
• The \(H\)-polynomial of a semisimple monoid.
• Betti Numbers of Toric Varieties and Eulerian Polynomials
• Combinatorics of Coxeter Groups
• THE GEOMETRY OF TORIC VARIETIES
• An Explicit Cell Decomposition of the Wonderful Compactification of a Semisimple Algebraic Group

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