Cell Classification of Gelfand $S_n$-Graphs

Abstract

Kazhdan and Lusztig introduced $W$-graphs to encode representations of Iwahori--Hecke algebras, and Marberg later introduced the broader class of Gelfand $W$-graphs. The molecules of the row Gelfand $S_n$-graph are classified by the row Beissinger insertion algorithm. We prove that these molecules are precisely the cells of the graph. The proof combines Greene's theorem with an adaptation of Nguyen's type A orderedness method.

21 pages