Publications of the Research Institute for Mathematical Sciences

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Volume 36, Issue 4, 2000, pp. 533–572
DOI: 10.2977/prims/1195142873

Zero actions and energy functions for perfect crystals

Timothy H. Baker[1]

(1) Research Institute for Mathematical Sciences, Kyoto University, 606-8502, KYOTO, JAPAN

We give a combinatorial description of the action of the crystal operators αΊ½0, f~0 on certain perfect crystals of U'q(Cn(1)), U'q(Dn(1)) and U'q(Dn+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.

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Baker Timothy: Zero actions and energy functions for perfect crystals. Publ. Res. Inst. Math. Sci. 36 (2000), 533-572. doi: 10.2977/prims/1195142873