Irreducible W-Graphs for Type D₄ and D₅

ABSTRACT

The “W-graph” concept was introduced by Kazhdan and Lusztig in their influential article Kazhdan and Lusztig (1979). If W is a Coxeter group, then a W-graph provides a method for constructing a matrix representation of the Hecke algebra ℋ associated with W (the degree of the representation being the number of vertices of the W-graph). The aim of this note is to explicitly construct all the irreducible representations of ℋ when W is of type D ₄ and D ₅.

Key Words:

• Character table
• Coxeter group
• Hecke algebra
• W-graph

2000 Mathematics Subject Classification:

• Primary and Secondary 20C08

ACKNOWLEDGMENTS

The author wishes to thank R. B. Howlett for his suggestions, which signifi-cantly improved the presentation of the article.

Notes

Communicated by B. Parshall.