Formal Characters and Resolutions of Certain Simple Infinite Dimensional $A_n$-Modules

Frank Lemire (emire@uwindsor.ca)
University of Windsor
401 Sunset Ave.
Windsor, Ontario N9B 3P4

Abstract

If $V$ is a finite dimensional simple module for a simple Lie algebra Berstein, Gel'fand, Gel'fand provided a formal character formula for $V$ as well as a resolution of $V$ in terms of Verma modules. In this talk we generalize these results to certain simple infinite dimensional $A_n$-modules having bounded weight multiplicities.