# Noon lecture

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On 14.11.2013 at 12:20 in S6, there is the following noon lecture:

# A combinatorial model for Kirillov-Reshetikhin crystals and applications

## Cristian Lenart

## Max-Planck-Institut fur Mathematik (Germany) and State University of New York at Albany (USA)

## Abstract

Crystals are colored directed graphs encoding information about Lie algebra representations. Certain crystals for affine Lie algebras called Kirillov-Reshetikhin (KR) crystals are graded by the energy function. Given a tensor product of KR crystals, there is a unique crystal isomorphism commuting tensor factors, which is called the combinatorial R-matrix. In Lie type A, the vertices of a tensor product of KR crystals are indexed by column-strict fillings (with 1,...,n) of a Young diagram. The energy is computed by the Lascoux-Schutzenberger charge statistic on fillings. The combinatorial R-matrix is realized by Schutzenberger's sliding game (jeu de taquin) on two columns. I will present a combinatorial model which generalizes these constructions uniformly across all Lie types. The talk is largely self-

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