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### Robinson-Schensted-Knuth via quiver representations

**Algebra & Discrete Mathematics**

Speaker: | Hugh Thomas, UQAM |

Related Webpage: | http://www.math.uqam.ca/une_page.php?id=72 |

Location: | 2112 MSB |

Start time: | Mon, Nov 6 2017, 4:15PM |

The Robinson-Schensted-Knuth correspondence is a many-faceted jewel of algebraic combinatorics. In one variation, it provides a bijection between permutations of n and pairs of standard Young tableaux with the same shape, which is a partition of n. In another (more general) version, it provides a bijection between fillings of a partition lambda by arbitrary non-negative integers and fillings of the same shape lambda by non-negative integers which weakly increase along rows and down columns (i.e., reverse plane partitions of shape lambda). I will discuss an interpretation of RSK in terms of the representation theory of type A quivers (i.e., directed graphs obtained by orienting a path graph). This allows us to generalize RSK to other Dynkin types (plus a choice of minuscule weight), and is related to periodicity results for piecewise-linear toggling. I will not assume familiarity with either RSK or with quiver representations. This is joint work with Al Garver and Becky Patrias.

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