Three combinatorial models for affine sl(n) crystals, with applications to cylindric plane partitions

Peter Tingley, University of California, Berkeley
Fine Hall 214

We discuss three combinatorial models for affine sl(n) crystals parametrized by partitions, configurations of beads on an "abacus," and cylindric plane partitions, respectively. These are reducible, but we can identify an irreducible subcrystal corresponding to any dominant integral highest weight. The cylindric plane partition model can in fact be viewed as the crystal for an irreducible affine gl(n) (as opposed to affine sl(n)) representation. Thus we can calculate the generating function for cylindric plane partitions using the Weyl character formula, recovering a recent result of A. Borodin. We also observe a form of rank level duality originally due to I. Frenkel.