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Tropical R maps and Affine Geometric Crystals
Masaki Kashiwara, Toshiki Nakashima, Masato Okado
By modifying the method in [KNO], certain affine geometric crystals are realized in affinization of the fundamental representation and the tropical R maps for the a…
Ultra-discretization of the G^(1)_2-Geometric Crystals to the D^(3)_4-Perfect Crystals
Toshiki Nakashima
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,θ) a ultra-discretization of X…
Affine Geometric Crystal of type
Toshiki Nakashima
We shall realize certain affine geometric crystal of type explicitly in the fundamental representation . Its explicit form is rather complicated but still…
Geometric Crystals on Unipotent Groups and Generalized Young Tableaux
Toshiki Nakashima
We define geometric/unipotent crystal structure on unipotent subgroups of semi-simple algebraic groups. We shall show that in -case, their ultra-discretizations coincide with…
Polyhedral Realizations of Crystal Bases for Modified Quantum Algebras of Type A
Ayumu Hoshino, Toshiki Nakashima
We describe the crystal bases of modified quantum algebras and its connected component containing ``zero vector''by the polyhedral realization method for the types A_n and A^(1)_1.…
Geometric Crystals on Schubert Varieties
Toshiki Nakashima
We define geometric crystals and unipotent crystals for arbitrary Kac-Moody groups and describe geometric and unipotent crystal structures on the Schubert varieties.