Structure of T Modules and Restricted Duals: The Classical and the Quantum Case

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.

Key Words:

• T modules
• Verma modules
• Category ℐ
• Restricted duals

Acknowledgments

This work is a part of the author's Ph.D. thesis and she expresses her sincere gratitude to her thesis advisor Professor Vinay Deodhar for his support and valuable discussions throughout her time as a graduate student and also for his continued interest and constant encouragement. Moreover, the author thanks Professor Vyjayanthi Chari for a question and the referee for suggestions that have both led to the present version of the paper and are greatly appreciated.