Rank 2 Affine Mv Polytopes
نویسندگان
چکیده
We give a realization of the crystal B(−∞) for ̂ sl2 using decorated polygons. The construction and proof are combinatorial, making use of Kashiwara and Saito’s characterization of B(−∞), in terms of the ∗ involution. The polygons we use have combinatorial properties suggesting they are the ̂ sl2 analogues of the Mirković-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 other rank 2 affine Kac-Moody algebra.
منابع مشابه
Mirkovic-vilonen Cycles and Polytopes
We give an explicit description of the Mirkovic-Vilonen cycles on the affine Grassmannian for arbitrary reductive groups. We also give a combinatorial characterization of the MV polytopes. We prove that a polytope is an MV polytope if and only if every 2-face of it is a rank 2 MV polytope.
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