An insight into the description of the crystal structure for Mirković-Vilonen polytopes

DOI10.1090/tran/6918zbMath1365.05295arXiv1501.07628OpenAlexW2963041100MaRDI QIDQ5267978

Yong Jiang, Jie Sheng

Publication date: 14 June 2017

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.07628

zbMATH Keywords

crystalpreprojective algebraMirković-Vilonen polytopediagram automorphism

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) 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) Representations of quivers and partially ordered sets (16G20) Simple, semisimple, reductive (super)algebras (17B20)

Related Items

Virtual crystals and Nakajima monomials, Virtualization map for the Littelmann path model, Rigged configurations and the \(\ast\)-involution

Cites Work

• Unnamed Item
• Unnamed Item
• Kac-Moody groups and cluster algebras
• A modification of the Anderson-Mirković conjecture for Mirković-Vilonen polytopes in types \(B\) and \(C\)
• Mirković-Vilonen cycles and polytopes.
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• The crystal base and Littelmann's refined Demazure character formula
• Some automorphisms of generalized Kac-Moody algebras
• Geometric construction of crystal bases
• A polytope calculus for semisimple groups.
• The crystal structure on the set of Mirković-Vilonen polytopes
• Geometric Langlands duality and representations of algebraic groups over commutative rings
• Parametrizations of Canonical Bases and Irreducible Components of Nilpotent Varieties
• Preprojective algebras and MV polytopes
• Mirković–Vilonen Polytopes and a Quiver Construction of Crystal Basis in Type A
• Canonical Bases Arising from Quantized Enveloping Algebras
• Mirković-Vilonen cycles and polytopes for a symmetric pair
• On the exceptional fibres of Kleinian singularities
• Irreducible components of varieties of modules