Minuscule Schubert varieties: poset polytopes, PBW-degenerated Demazure modules, and Kogan faces

DOI10.1007/s10468-015-9548-5zbMath1331.05225arXiv1410.1126OpenAlexW3106474851MaRDI QIDQ5962975

Rekha Biswal, Ghislain Fourier

Publication date: 25 February 2016

Published in: Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.1126

zbMATH Keywords

Schubert varietiesKogan facesPBW filtrationposet polytopes

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Grassmannians, Schubert varieties, flag manifolds (14M15) Classical problems, Schubert calculus (14N15)

Related Items (12)

PBW degenerate Schubert varieties: Cartan components and counterexamples ⋮ Homogeneous bases for Demazure modules ⋮ The PBW filtration and convex polytopes in type B ⋮ Favourable modules: filtrations, polytopes, Newton-Okounkov bodies and flat degenerations ⋮ Marked poset polytopes: Minkowski sums, indecomposables, and unimodular equivalence ⋮ Enriched chain polytopes ⋮ PBW filtration and monomial bases for Demazure modules in types A and C ⋮ PBW-degenerated Demazure modules and Schubert varieties for triangular elements ⋮ PBW-type filtration on quantum groups of type \(A_{n}\) ⋮ The degree of the Hilbert-Poincaré polynomial of PBW-graded modules ⋮ Marked chain-order polytopes ⋮ Schubert calculus from polyhedral parametrizations of Demazure crystals

Cites Work

• Unnamed Item
• The degree of the Hilbert-Poincaré polynomial of PBW-graded modules
• Nonsymmetric Macdonald polynomials and PBW filtration: towards the proof of the Cherednik-Orr conjecture
• PBW filtration and bases for irreducible modules in type \({\text{\textsf{A}}}_{n}\)
• Gelfand-Tsetlin polytopes and Feigin-Fourier-Littelmann-Vinberg polytopes as marked poset polytopes
• PBW-degenerated Demazure modules and Schubert varieties for triangular elements
• Two poset polytopes
• Cones, crystals, and patterns
• Hilbert functions of graded algebras
• The crystal base and Littelmann's refined Demazure character formula
• Degenerations of flag and Schubert varieties to toric varieties
• Vertices of Gelfand-Tsetlin polytopes
• Toric degenerations of spherical varieties
• Crystal graphs and Young tableaux
• Nonsymmetric difference Whittaker functions
• Favourable modules: filtrations, polytopes, Newton-Okounkov bodies and flat degenerations
• Extremal part of the PBW-filtration and nonsymmetric Macdonald polynomials
• Unimodular Equivalence of Order and Chain Polytopes
• New homogeneous ideals for current algebras: filtrations, fusion products and Pieri rules
• PBW-filtration over ℤ and Compatible Bases for V ℤ(λ) in Type A n and C n
• PBW Filtration and Bases for Symplectic Lie Algebras
• Schubert calculus and Gelfand-Zetlin polytopes
• PBW filtration: Feigin-Fourier-Littelmann modules via Hasse diagrams

This page was built for publication: Minuscule Schubert varieties: poset polytopes, PBW-degenerated Demazure modules, and Kogan faces