# Darstellungstheorietage and Nikolaus Conference 2013

Speaker: Thomas Gerber

Title: An Analogue of the Robinson-Schensted-Knuth Algorithm in Affine Type $$A$$

Abstract: The Robinson-Schensted-Knuth (RSK) insertion procedure has a natural interpretation in terms of crystals in type $$A$$. In this talk, I make explicit a particular crystal isomorphism for Fock spaces representations of $$\mathcal{U}_q(\widehat{\mathfrak{sl}_e})$$. This gives a combinatorial procedure generalising the RSK correspondence to the affine case.