An algebraic cell decomposition of the nonnegative part of a flag variety

DOI10.1006/jabr.1998.7665zbMath0920.20041arXivalg-geom/9709035OpenAlexW2092231151MaRDI QIDQ1283666

Konstanze Rietsch

Publication date: 21 April 1999

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

Full work available at URL: https://arxiv.org/abs/alg-geom/9709035

zbMATH Keywords

Weyl groupsflag varietiestotal positivityreductive linear algebraic groupsvarieties of Borel subgroupsreal algebraic morphisms

Mathematics Subject Classification ID

Representation theory for linear algebraic groups (20G05) Group actions on varieties or schemes (quotients) (14L30) Grassmannians, Schubert varieties, flag manifolds (14M15) Linear algebraic groups over the reals, the complexes, the quaternions (20G20)

Related Items (23)

Bridge graphs and Deodhar parametrizations for positroid varieties ⋮ Cluster structures on strata of flag varieties ⋮ Total positivity for the Lagrangian Grassmannian ⋮ Edge vectors on plabic networks in the disk and amalgamation of totally non-negative Grassmannians ⋮ Bruhat interval polytopes ⋮ Reducible \(M\)-curves for Le-networks in the totally-nonnegative Grassmannian and KP-II multiline solitons ⋮ On two notions of total positivity for partial flag varieties ⋮ Totally nonnegative Grassmannians, Grassmann necklaces, and quiver Grassmannians ⋮ Regularity theorem for totally nonnegative flag varieties ⋮ Gradient flows, adjoint orbits, and the topology of totally nonnegative flag varieties ⋮ Positive geometries and canonical forms ⋮ The totally nonnegative part of \(G/P\) is a ball ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Positive configuration space ⋮ A positive Grassmannian analogue of the permutohedron ⋮ Moment curves and cyclic symmetry for positive Grassmannians ⋮ The totally nonnegative Grassmannian is a ball ⋮ Unnamed Item ⋮ The totally nonnegative part of \(G/P\) is a CW complex ⋮ Flag manifolds over semifields ⋮ A Mirror Construction for the Totally Nonnegative Part of the Peterson Variety ⋮ Ising model and the positive orthogonal Grassmannian

Cites Work

• On some geometric aspects of Bruhat orderings. I: A finer decomposition of Bruhat cells
• Representations of Coxeter groups and Hecke algebras
• Introduction to quantum groups
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