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

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2015
• Main Authors: Coulembier, K., Mazorchuk, V.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2015
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146993
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules / K. Coulembier, V. Mazorchuk // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 51 назв. — англ.

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 ca...