2020/01/31 by Kailash C. Misra, Misra, Kailash C., Suchada Pongprasert +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.RT #msc:17B10 #msc:17B37 #msc:17B67
paper · pdf · doi:10.48550/arxiv.2002.00007
arXiv admin note: substantial text overlap with arXiv:1812.01651
arxiv created 2020/01/31 · arxiv updated 2020/02/04
Let \mathfrak g be an affine Lie algebra with index set I = \0, 1, 2, ⋯ , n\. It is conjectured in \citeKNO that for each Dynkin node k ∈ I ∖ \0\ the affine Lie algebra \mathfrak g has a positive geometric crystal whose ultra-discretization is isomorphic to the limit of a coherent family of perfect crystals for the Langland dual \mathfrak g L. In this paper we show that at the spin node k=6, the family of perfect crystals given in \citeKMN2 form a coherent family and show that its limit B6,∞ is isomorphic to the ultra-discretization of the positive geometric crystal we constructed in \citeMP for the affine Lie algebra D6(1) which proves the conjecture in this case.