Involutions on Standard Young Tableaux and Divisors on Metric Graphs

Abstract

We elaborate upon a bijection discovered by Cools, Draisma, Payne, and Robeva (2012) between the set of rectangular standard Young tableaux and the set of equivalence classes of chip configurations on certain metric graphs under the relation of linear equivalence. We present an explicit formula for computing the $v_0$-reduced divisors (representatives of the equivalence classes) associated to given tableaux, and use this formula to prove (i) evacuation of tableaux corresponds (under the bijection) to reflecting the metric graph, and (ii) conjugation of the tableaux corresponds to taking the Riemann-Roch dual of the divisor.