Involutions on standard Young tableaux and divisors on metric graphs

• Main Authors: Agrawal, Rohit (Author), Musiker, Gregg (Author), Sotirov, Vladimir (Author), Wei, Fan (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: Electronic Journal of Combinatorics, 2014-09-17T12:00:50Z.
• Subjects: Article
• Online Access: Get fulltext

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[subscript 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.
National Science Foundation (U.S.) (Grant DMS-1001933)
National Science Foundation (U.S.) (Grant DMS-1067183)
National Science Foundation (U.S.) (Grant DMS-1148634)