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Robinson-Schensted-Knuth via quiver representations

Algebra & Discrete Mathematics

Speaker: Hugh Thomas, UQAM
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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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