2012/09/20 by Kailash C. Misra, Toshiki Nakashima, Misra, Kailash C. +1 · 1 citation
Mathematics · #14M15 #17B37 #17B67 #22E65 #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:14M15 #msc:17B37 #msc:17B67 #msc:22E65
paper · pdf · doi:10.48550/arxiv.1209.4565
18 pages. arXiv admin note: substantial text overlap with arXiv:1003.1242, arXiv:0712.3894, arXiv:math/0612858, arXiv:0911.3556
arxiv created 2012/09/20 · arxiv updated 2012/09/21
Let g be an affine Lie algebra with index set I = \0, 1, 2,..., n\ and gL be its Langlands dual. It is conjectured that for each i ∈ I ∖ \0\ the affine Lie algebra g has a positive geometric crystal whose ultra-discretization is isomorphic to the limit of certain coherent family of perfect crystals for gL. We prove this conjecture for i=2 and g = An(1).