Rank 2 affine MV polytopes

2012/02/29 by Pierre Baumann, Baumann, Pierre, Thomas Dunlap +5
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #math.CO #math.QA

paper · pdf · doi:10.48550/arxiv.1202.6416

24 pages

arxiv created 2012/02/29 · arxiv updated 2012/03/01

Abstract

We give a realization of the infinity crystal for affine sl(2) using decorated polygons. The construction and proof are combinatorial, making use of Kashiwara and Saito's characterization of the infinity crystal in terms of the * involution. The polygons we use have combinatorial properties suggesting they are the analogues in this case of the Mirkovic-Vilonen polytopes defined by Anderson and the third author in finite type. Using Kashiwara's similarity of crystals we also give MV polytopes for A₂⁽²⁾, the only other rank two affine Kac-Moody algebra.

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• Affine PBW Bases and MV Polytopes in Rank 2
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