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Insertion algorithms for Type $\mathrm{B}$ and $\mathrm{D}$ Gelfand $W$-graphs

Yifeng Zhang

Abstract

Like the RSK correspondence for symmetric groups, Garfinkle defined a domino correspondence for type $\mathrm{B}$ and $\mathrm{D}$ 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 $\mathrm{B}$ 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 $\mathrm{B}$ and $\mathrm{D}$ Coxeter groups.

Insertion algorithms for Type $\mathrm{B}$ and $\mathrm{D}$ Gelfand $W$-graphs

Abstract

Like the RSK correspondence for symmetric groups, Garfinkle defined a domino correspondence for type and 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 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 -graphs for type and Coxeter groups.
Paper Structure (4 sections, 2 equations)

This paper contains 4 sections, 2 equations.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Domino correspondence
  4. Domino tableaux

Theorems & Definitions (1)

  • Example 3.1