Rank 2 affine MV polytopes

DOI10.1090/S1088-4165-2013-00438-7zbMath1302.17037arXiv1202.6416MaRDI QIDQ2937173

Peter Tingley, Thomas Dunlap, Pierre Baumann, Joel Kamnitzer

Publication date: 8 January 2015

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

Full work available at URL: https://arxiv.org/abs/1202.6416

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Combinatorial aspects of representation theory (05E10) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)

Related Items (6)

Affine PBW bases and affine MV polytopes ⋮ Perfect bases in representation theory: three mountains and their springs ⋮ Affine PBW bases and MV polytopes in rank 2 ⋮ Unnamed Item ⋮ Affine Mirković-Vilonen polytopes ⋮ Mirkovic-Vilonen polytopes and Khovanov-Lauda-Rouquier algebras

Cites Work

• Double MV cycles and the Naito-Sagaki-Saito crystal.
• Affine Mirković-Vilonen polytopes
• Mirković-Vilonen cycles and polytopes.
• A basis of type Poincaré-Birkhoff-Witt for the quantum algebra of \(\widehat{sl}(2)\)
• The crystal base and Littelmann's refined Demazure character formula
• Geometric construction of crystal bases
• A polytope calculus for semisimple groups.
• An algebraic characterization of the affine canonical basis
• The crystal structure on the set of Mirković-Vilonen polytopes
• Affine PBW bases and MV polytopes in rank 2
• Toward Berenstein-Zelevinsky data in affine type $A$, I: Construction of affine analogs
• Introduction to quantum groups
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