Demazure Modules, Chari–Venkatesh Modules and Fusion Products
Let g be a finite-dimensional complex simple Lie algebra with highest root θ. Given two non-negative integers m, n, we prove that the fusion product of m copies of the level one Demazure module D(1,θ) with n copies of the adjoint representation ev₀V(θ) is independent of the parameters and we give ex...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2014 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2014
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146400 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Demazure Modules, Chari–Venkatesh Modules and Fusion Products / B. Ravinder // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 10 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862736116244807680 |
|---|---|
| author | Ravinder, B. |
| author_facet | Ravinder, B. |
| citation_txt | Demazure Modules, Chari–Venkatesh Modules and Fusion Products / B. Ravinder // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 10 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Let g be a finite-dimensional complex simple Lie algebra with highest root θ. Given two non-negative integers m, n, we prove that the fusion product of m copies of the level one Demazure module D(1,θ) with n copies of the adjoint representation ev₀V(θ) is independent of the parameters and we give explicit defining relations. As a consequence, for g simply laced, we show that the fusion product of a special family of Chari-Venkatesh modules is again a Chari-Venkatesh module. We also get a description of the truncated Weyl module associated to a multiple of θ.
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| first_indexed | 2025-12-07T19:52:10Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-146400 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:52:10Z |
| publishDate | 2014 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ravinder, B. 2019-02-09T10:56:05Z 2019-02-09T10:56:05Z 2014 Demazure Modules, Chari–Venkatesh Modules and Fusion Products / B. Ravinder // Symmetry, Integrability and Geometry: Methods and Applications. — 2014. — Т. 10. — Бібліогр.: 10 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B67; 17B10 DOI:10.3842/SIGMA.2014.110 https://nasplib.isofts.kiev.ua/handle/123456789/146400 Let g be a finite-dimensional complex simple Lie algebra with highest root θ. Given two non-negative integers m, n, we prove that the fusion product of m copies of the level one Demazure module D(1,θ) with n copies of the adjoint representation ev₀V(θ) is independent of the parameters and we give explicit defining relations. As a consequence, for g simply laced, we show that the fusion product of a special family of Chari-Venkatesh modules is again a Chari-Venkatesh module. We also get a description of the truncated Weyl module associated to a multiple of θ. The author thanks Vyjayanthi Chari, K.N. Raghavan and S. Viswanath for many helpful discussions
 and encouragement. Part of this work was done when the author was visiting the Centre de
 Recherche Mathematique (CRM), Montreal, Canada, during the thematic semester on New Directions
 in Lie Theory. The author acknowledges the hospitality and financial support extended
 to him by CRM. The author also thanks the anonymous referees for their valuable comments,
 due to which the paper is much improved. The author acknowledges support from CSIR under
 the SPM Fellowship scheme en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Demazure Modules, Chari–Venkatesh Modules and Fusion Products Article published earlier |
| spellingShingle | Demazure Modules, Chari–Venkatesh Modules and Fusion Products Ravinder, B. |
| title | Demazure Modules, Chari–Venkatesh Modules and Fusion Products |
| title_full | Demazure Modules, Chari–Venkatesh Modules and Fusion Products |
| title_fullStr | Demazure Modules, Chari–Venkatesh Modules and Fusion Products |
| title_full_unstemmed | Demazure Modules, Chari–Venkatesh Modules and Fusion Products |
| title_short | Demazure Modules, Chari–Venkatesh Modules and Fusion Products |
| title_sort | demazure modules, chari–venkatesh modules and fusion products |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146400 |
| work_keys_str_mv | AT ravinderb demazuremodulescharivenkateshmodulesandfusionproducts |