Zero Action on Perfect Crystals for U_q(G_2^{(1)})

Abstract

The actions of 0-Kashiwara operators on the $U_q^{\prime }(G_2^{(1)})$-crystal $B_l$ in [Yamane S., J. Algebra 210 (1998), 440-486] are made explicit by using a similarity technique from that of a $U_q^{\prime }(D_4^{(3)})$-crystal. It is shown that $\{B_l{\}}_{l\ge 1}$ forms a coherent family of perfect crystals.

References in corpus (1)

• Perfect Crystals for U_q(D_4^{(3)})

Cited by in corpus (6)

• Crystal energy functions via the charge in types A and C
• A crystal to rigged configuration bijection and the filling map for type $D_4^{(3)}$
• Soliton cellular automaton associated with $G_2^{(1)}$ crystal base
• Soliton cellular automaton associated with $D_n^{(1)}$-crystal $B^{2,s}$
• Ultra-discretization of the D_4^3-Geometric Crystals to the G_2^1-Perfect Crystals
• An Explicit Algorithm of Rigged Configuration Bijection for the Adjoint Crystal of Type $G_2^{(1)}$