# Mathematics Colloquia and Seminars

### Three combinatorial models for $\widehat{sl}_n$ crystals, with applications to cylindric plane partitions
We define three combinatorial models for $\widehat{sl}_n$ 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 $\Lambda$. Cyclic plane partitions actually parametrize a basis for $V_\Lambda \otimes F$, where $F$ is the space spanned by partitions. We use this to calculate the partition function for a system of random cylindric plane partitions. We also observe a form of weight level duality.