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

Kevin Coulembier ; Volodymyr Mazorchuk

Symmetry, integrability and geometry: methods and applications, Tome 11 (2015)

Résumé

We prove that the categories of Gelfand–Zeitlin modules of $\mathfrak{g}=\mathfrak{gl}_n$ and Whittaker modules associated with a semi-simple complex finite-dimensional algebra $\mathfrak{g}$ are extension full in the category of all $\mathfrak{g}$-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.

Détail

Keywords: extension fullness; Gelfand–Zeitlin modules; Whittaker modules; Yoneda extensions; homological dimension.

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