Completely Positive Maps for Imprimitive Reflection Groups

TL;DR

This paper constructs completely positive maps for imprimitive reflection groups and uses them to define creation and annihilation operators on Fock space, advancing the mathematical framework for quantum symmetries.

Contribution

It introduces new completely positive quasimultiplicative maps for imprimitive reflection groups and applies them to define operators on Fock space.

Findings

Existence of completely positive quasimultiplicative maps for these groups

Definition of creation and annihilation operators on Fock space using these maps

Potential applications in quantum symmetry analysis

Abstract

This article proves the existence of completely positive quasimultiplicative maps from the group algebra of imprimitive reflection groups to the set of bounded operators, and uses those linear maps to define creation and annihilation operators on the full Fock space.