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arXiv · 1409.5717

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

Kevin Coulembier·Volodymyr Mazorchuk
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Abstract

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.

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Kevin Coulembier, Volodymyr Mazorchuk. 2014-09-19. Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules. https://doi.org/10.3842/sigma.2015.016

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