Séminaire Lotharingien de Combinatoire, 84B.48 (2020), 12 pp.

Laura Colmenarejo, Rosa Orellana, Franco Saliola, Anne Schilling and Mike Zabrocki

An Insertion Algorithm for Diagram Algebras

Abstract. We generalize the Robinson-Schensted-Knuth algorithm to the insertion of two row arrays of multisets. This generalization leads to an algorithm from partition diagrams to pairs of a standard tableau and a standard multiset tableau of the same shape, which has the remarkable property that it is well-behaved with respect to restricting a representation to a subalgebra. This insertion algorithm matches recent representation-theoretic results of Halverson and Jacobson.

Received: November 20, 2019. Accepted: February 20, 2020. Final version: April 30, 2020.

The following versions are available: