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An RSK correspondence in affine type A

Hugh Thomas

In recent work with Al Garver and Becky Patrias, arXiv:1812.08345, we showed how the Robinson–Schensted–Knuth correspondence could be interpreted in terms of representations of a type A quiver. In that same paper, we also discussed how to extend the RSK correspondence to other Dynkin types. In the present talk, I will pursue the generalization of RSK in another direction, namely into affine type A. While we are again motivated by quiver representations, in this talk the quivers will be almost entirely in the background, and I will focus on the combinatorics which we have uncovered. This talk is based on ongoing joint work by the same team of authors.