Department of Mathematics and Statistics

Department of Mathematics and Statistics
Department of Mathematics and Statistics

Geometry and Representation Theory Seminar


Monday, March 5th, 2018

Time: 4:30 p.m.  Place: Jeffery Hall 319

Speaker: Hugh Thomas (UQAM)

Title: The Robinson-Schensted-Knuth correspondence via quiver representations

Abstract:  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.