Symmetry, Integrability and Geometry: Methods and Applications (Mar 2010)

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

  • Kailash C. Misra,
  • Mahathir Mohamad,
  • Masato Okado

Journal volume & issue
Vol. 6
p. 022


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The actions of 0-Kashiwara operators on the U_q(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'(D_4^{(3)})-crystal. It is shown that {B_l}_{l ≥ 1} forms a coherent family of perfect crystals.