Ultra-discretization of the G^(1)_2-Geometric Crystals to the D^(3)_4-Perfect Crystals

Details Ultra-discretization of the G^(1)_2-Geometric Crystals to the D^(3)_4-Perfect Crystals Ultra-discretization of the G^(1)_2-Geometric Crystals to the D^(3)_4-Perfect Crystals

2007-12-23

arxiv.org/abs/0712.3894v1

Mathematics

Quantum Algebra

19 pages

Scientific paper

We obtain the affirmative answer to the conjecture in [15]. More precisely,
let X be the affine geometric crystal of type G^(1)_2 in [15] and
UD(X,T,\theta) a ultra-discretization of X with respect to a certain positive
structure \theta. Then we show that UD(X,T,\theta) is isomorphic to the limit
of coherent family of perfect crystals of type D^(3)_4 in [7].

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