REPRESENTATION THEORY OF ALGEBRAIC GROUPS AND QUANTUM GROUPS 284 273-296 2010年 [査読有り]
We obtain the affirmative answer to the conjecture in [14]. More precisely, let chi := (V, {e(i)}, {gamma(i)}, {epsilon(i})) be the affine geometric crystal of type G(2)((1)) in [14] and U D (chi, T, theta) a ultra-discretization of chi with respe...
and Prehomogeneous Geometric Crystals (New Trends in Combinatorial Representation Theory)" target="_blank">Universal Tropical R map of and Prehomogeneous Geometric Crystals (New Trends in Combinatorial Representation Theory)
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 360(7) 3645-3686 2008年 [査読有り]
For every non- exceptional a. ne Lie algebra, we explicitly construct a positive geometric crystal associated with a fundamental representation. We also show that its ultra- discretization is isomorphic to the limit of certain perfect crystals of ...
LIE ALGEBRAS, VERTEX OPERATOR ALGEBRAS AND THEIR APPLICATIONS 442 179-192 2007年 [査読有り]
We shall realize certain affine geometric crystal of type G(2)((1)) ex plicitly in the fundamental representation W(pi(1)). Its explicit form is rather complicated but still keeps positive structure.
上智大学
理工学部