We give a combinatorial description of the action of the crystal operators _ẽ_0, f~0 on certain perfect crystals of U'q(C__n(1)), U'q(D__n(1)) and U'q(D__n+1(2)), by means of Dynkin diagram automorphisms and Schensted column insertion. Also, for certain level 1 perfect crystals of these algebras we give a definition of a combinatorial "charge" related to the energy function on homogeneous paths in such crystals.
Cite this article
Timothy H. Baker, Zero actions and energy functions for perfect crystals. Publ. Res. Inst. Math. Sci. 36 (2000), no. 4, pp. 533–572DOI 10.2977/PRIMS/1195142873