Preprojective algebras and MV polytopes

DOI10.1090/S1088-4165-2012-00413-7zbMath1242.05273arXiv1009.2469MaRDI QIDQ2889348

Pierre Baumann, Joel Kamnitzer

Publication date: 7 June 2012

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

Full work available at URL: https://arxiv.org/abs/1009.2469

zbMATH Keywords

Lusztig's nilpotent varieties

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Semisimple Lie groups and their representations (22E46) Representations of quivers and partially ordered sets (16G20)

Related Items

Affine PBW bases and affine MV polytopes, Loop Grassmannians of Quivers and Affine Quantum Groups, Modules with 1-Dimensional Socle and Components of Lusztig Quiver Varieties in Type A, Toda systems, cluster characters, and spectral networks, On deformed preprojective algebras, Classifying tilting complexes over preprojective algebras of Dynkin type, Quivers with relations for symmetrizable Cartan matrices. I: Foundations, Pro-species of algebras. I: Basic properties, Symplectic resolutions, symplectic duality, and Coulomb branches, Tropical F$F$‐polynomials and general presentations, Applications of spherical twist functors to Lie algebras associated to root categories of preprojective algebras, Affine PBW bases and MV polytopes in rank 2, Weyl group action and semicanonical bases, Unnamed Item, The transition matrix between PBW basis and semicanonical basis of \(U^+(\mathfrak{s}\mathfrak{l}_n(\mathbb C))\), Affine Mirković-Vilonen polytopes, Mirkovic-Vilonen polytopes and Khovanov-Lauda-Rouquier algebras, PBW parametrizations and generalized preprojective algebras, Torsion pairs for quivers and the Weyl groups, Quotient closed subcategories of quiver representations, Equivariant multiplicities of simply-laced type flag minors, An insight into the description of the crystal structure for Mirković-Vilonen polytopes

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