Cell Classification of Gelfand S_n-Graphs

2025/03/27 by Zhang, Yifeng
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2503.21215

Abstract

Kazhdan and Lusztig introduced the W-graphs, which represent the multiplication action of the standard basis on the canonical bais in the Iwahori-Hecke algebra. In the Hecke algebra module, Marberg defined two generalied W-graphs, called the Gelfand W-graphs. The classification of the molecules of the type A Gelfand S_n-graphs are determined by two RSK-like insertion algorithms. We finish the classification of cells by proving that every molecule in the S_n-graphs is indeed a cell.

Related

• Type A Molecules are Kazhdan-Lusztig
• Lusztig a-functions for quasiparabolic sets
• Insertion algorithms for Type B and D Gelfand W-graphs
• Type A-admissible cells are Kazhdan-Lusztig
• Combinatorial Gelfand Models