Gelfand models for classical Weyl groups

In a recent preprint Kodiyalam and Verma give a particularly simple Gelfand model for the symmetric group that is built naturally on the space of involutions. In this manuscript we give a natural extension of Kodiyalam and Verma's model to a Gelfand model for Weyl groups of type Bn and D2n+1. Then we define an explicit isomorphism between this Gelfand model and the polynomial model using a technique we call telescopic decomposition.