Rank 2 affine MV polytopes

Details Rank 2 affine MV polytopes Rank 2 affine MV polytopes

2012-02-29

arxiv.org/abs/1202.6416v1

Mathematics

Combinatorics

24 pages

Scientific paper

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 $A_2^{(2)}$, the only other rank two affine Kac-Moody algebra.

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