Noncommutative probability of type D

TL;DR

This paper introduces a new noncommutative probability framework based on Coxeter groups of type D, constructing a deformed Fock space and Brownian motion analogous to existing models for types A and B.

Contribution

It develops a novel noncommutative probability model for Coxeter groups of type D, expanding the scope of deformed Fock spaces and associated stochastic processes.

Findings

Constructed a deformed Fock space for type D Coxeter groups.

Defined a Brownian motion associated with this new framework.

Established parallels with type A and B noncommutative probability models.

Abstract

We construct a deformed Fock space and a Brownian motion coming from Coxeter groups of type D. The construction is analogous to that of the $q$-Fock space (of type A) and the $(\alpha,q)$-Fock space (of type B).