Gelfand models for classical Weyl groups

TL;DR

This paper extends a simple Gelfand model from symmetric groups to Weyl groups of types B and D, providing explicit isomorphisms and a novel telescopic decomposition technique.

Contribution

It introduces a natural extension of the Gelfand model to Weyl groups of types B and D, and defines an explicit isomorphism with the polynomial model.

Findings

Extended Gelfand models for Weyl groups of types B and D

Established explicit isomorphism with polynomial models

Introduced telescopic decomposition technique

Abstract

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 B_{n} and D_{2n+1}. Then we define an explicit isomorphism between this Gelfand model and the polynomial model using a technique that we call telescopic decomposition.