Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2015 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146993 |
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| 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862706365411098624 |
|---|---|
| author | Coulembier, K. Mazorchuk, V. |
| author_facet | Coulembier, K. Mazorchuk, V. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T16:58:50Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146993 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:58:50Z |
| publishDate | 2015 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Coulembier, K. Mazorchuk, V. 2019-02-12T18:05:03Z 2019-02-12T18:05:03Z 2015 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. 1815-0659 2010 Mathematics Subject Classification: 16E30; 17B10 DOI:10.3842/SIGMA.2015.016 https://nasplib.isofts.kiev.ua/handle/123456789/146993 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. This paper is a contribution to the Special Issue on New Directions in Lie Theory. The full collection is
 available at http://www.emis.de/journals/SIGMA/LieTheory2014.html.
 KC is a Postdoctoral Fellow of the Research Foundation – Flanders (FWO). VM is partially
 supported by the Swedish Research Council. A substantial part of this work was done during
 the visit of the authors to the CRM Thematic Semester “New Directions in Lie Theory” in
 Montreal. We thank CRM for hospitality and partial support. We thank the referees for helpful
 comments. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules Article published earlier |
| spellingShingle | Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules Coulembier, K. Mazorchuk, V. |
| title | Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules |
| title_full | Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules |
| title_fullStr | Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules |
| title_full_unstemmed | Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules |
| title_short | Extension Fullness of the Categories of Gelfand-Zeitlin and Whittaker Modules |
| title_sort | extension fullness of the categories of gelfand-zeitlin and whittaker modules |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146993 |
| work_keys_str_mv | AT coulembierk extensionfullnessofthecategoriesofgelfandzeitlinandwhittakermodules AT mazorchukv extensionfullnessofthecategoriesofgelfandzeitlinandwhittakermodules |