01/23/2024
By Emily Gunawan
Wednesday, Jan. 23, 11 a.m. to noon in Southwick Hall Conference Room 350W.
Speaker: Benjamin Dequêne (University of Picardie Jules Verne)
Title: A generalized RSK correspondence via the combinatorics of (type A) quiver representations
Abstract: The Robinson-Schensted-Knuth correspondence is a bijection from nonnegative integer matrices to pairs of semi-standard Young tableaux. A generalized version of RSK gives a bijection from fillings of a tableau of shape lambda to reverse plane partitions of shape lambda.
From the quiver representation point of view, the RSK correspondence provides a transformation between two different invariants of a module X (in a certain subcategory). The entries in the arbitrary filling of shape lambda correspond to multiplicities of indecomposable summands of the representation, while the entries in the reverse plane partition of shape lambda record the generic Jordan form data of X, an invariant introduced by Garver, Patrias, and Thomas.
My talk aims to present a version of RSK that works from the most general possible choice of a subcategory of the category of representations of a type A quiver. Note that this talk will not assume that the audience has prior knowledge of quiver representations.
This work is a combinatorial extraction (in progress) of my Ph.D. work, supervised by Hugh Thomas.
For more information, see Mathematics and Statistics Seminar Talks.