Perforated Tableaux in Type A_n-1 Crystal Graphs and the RSK Correspondence

2022/09/27 by Appleby, Glenn D., Whitehead, Tamsen
#05E10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.13633

Abstract

We continue work begun in \citeptab which introduced perforated tableaux as a combinatorial model for crystals of type A_n-1, emphasizing connections to the classical Robinson-Schensted-Knuth (RSK) correspondence and Lusztig involutions, and, more generally, exploring the role of insertion schemes in the analysis of crystal graphs. An essential feature of our work is the role of dual crystals (\citeGerberLecouvey,vanLeeuwen) from which we obtain new results within and beyond the classic RSK theory.

Related

• Perforated Tableaux: A Combinatorial Model for Crystal Graphs in Type A_n-1
• Double crystals of binary and integral matrices
• On the Combinatorics of Crystal Graphs, I. Lusztig's Involution
• An action of the cactus group of shifted tableau crystals
• Crystal skeletons: Combinatorics and axioms