2023/11/30 by Zhang, Yifeng
#Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2312.14043
Like the RSK correspondence for symmetric groups, Garfinkle defined a domino correspondence for type B and D Coxeter groups. Similar to the Knuth relations, Taskin and Pietraho give the plactic relations for the domino correspondence and Bonnafé use them to classify the cells for type B Coxeter groups. We give some further properties of the plactic relations and use these relations to describe the bidirected edges and the molecules of Gelfand W-graphs for type B and D Coxeter groups.