Perforated Tableaux in Type An-1 Crystal Graphs and the RSK Correspondence
Abstract
We continue work begun in ptab which introduced perforated tableaux as a combinatorial model for crystals of type An-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 (GerberLecouvey,vanLeeuwen) from which we obtain new results within and beyond the classic RSK theory.
0