Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules

Abstract

We prove that the categories of Gelfand-Zeitlin modules of g=gln and Whittaker modules associated with a semi-simple complex finite-dimensional algebra g are extension full in the category of all g-modules. This is used to estimate and in some cases determine the global dimension of blocks of the categories of Gelfand-Zeitlin and Whittaker modules.