Mirković-Vilonen polytopes lying in a Demazure crystal and an opposite Demazure crystal

DOI10.1016/j.aim.2009.03.008zbMath1194.17008arXiv0806.3112OpenAlexW2008077791MaRDI QIDQ1028349

Satoshi Naito, Daisuke Sagaki

Publication date: 30 June 2009

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.3112

zbMATH Keywords

quantum grouppolytopecrystal basecrystalDemazure crystalDemazure model

Mathematics Subject Classification ID

Special polytopes (linear programming, centrally symmetric, etc.) (52B12) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Grassmannians, Schubert varieties, flag manifolds (14M15) Classical groups (algebro-geometric aspects) (14L35) Cohomology theory for linear algebraic groups (20G10)

Related Items

Relating the right key to the type A filling map and minimal defining chains, Modules with 1-Dimensional Socle and Components of Lusztig Quiver Varieties in Type A, Polytopal estimate of Mirković-Vilonen polytopes lying in a Demazure crystal, Weight polytopes and saturation of Demazure characters

Cites Work

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• Piecewise linear parametrization of canonical bases
• Equidimensionality of convolution morphisms and applications to saturation problems.
• A modification of the Anderson-Mirković conjecture for Mirković-Vilonen polytopes in types \(B\) and \(C\)
• Mirković-Vilonen cycles and polytopes.
• Cones, crystals, and patterns
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras
• The crystal base and Littelmann's refined Demazure character formula
• A polytope calculus for semisimple groups.
• Perverse sheaves on affine Grassmannians and Langlands duality
• Tensor product multiplicities, canonical and totally positive varieties
• Crystals via the affine Grassmannian
• The crystal structure on the set of Mirković-Vilonen polytopes
• Geometric Langlands duality and representations of algebraic groups over commutative rings
• Quiver varieties and Demazure modules
• Braid group action and canonical bases
• Combinatorics of Coxeter Groups
• Galleries, Hall-Littlewood polynomials, and structure constants of the spherical Hecke algebra
• On Mirković-Vilonen cycles and crystal combinatorics
• Mirković-Vilonen cycles and polytopes for a symmetric pair
• Convexity and Commuting Hamiltonians
• Polytopes for Crystallized Demazure Modules and Extremal Vectors
• Affine Weyl Groups in K-Theory and Representation Theory
• Introduction to quantum groups
• Lakshmibai-Seshadri paths fixed by a diagram automorphism.