Publications of the Research Institute for Mathematical Sciences
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Zero actions and energy functions for perfect crystalsTimothy H. Baker (1) Research Institute for Mathematical Sciences, Kyoto University, 606-8502, KYOTO, JAPAN
We give a combinatorial description of the action of the crystal operators ẽ0, 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