Structure of T modules and restricted duals: the classical and the quantum case

TL;DR

This paper provides a concrete realization of Enright's T modules, demonstrating their self-duality and identifying the restricted duals of Verma modules in both classical and quantum contexts.

Contribution

It introduces a concrete realization of T modules, proving their self-duality and characterizing the restricted duals of Verma modules in classical and quantum cases.

Findings

T modules are explicitly realized.

T modules are shown to be self-dual.

Restricted duals of Verma modules are identified.

Abstract

A concrete realization of Enright's $T$ modules is obtained. This is used to show their self-duality. As a consequence, the restricted duals of Verma modules are also identified.