| This paper presents some specific matrix representations of Coxeter groups of type D. To accomplish this, we describe how to construct an orthonormal basis for each irreducible representation, and produce a set of orthogonal matrices relative to that basis. In a second construction, we find a diagonal change of basis that produces matrices with rational entries.; By using hereditary bases, we are guaranteed that the matrices constructed will be sparse, and also that the matrix entries in the orthogonal case are canonical up to sign.; Similar matrix representations have been previously produced for the Coxeter groups of type A, type B/C, and the exceptional Weyl groups. This work completes the construction of explicit matrices for the irreducible representations of all finite Weyl groups. |
