| Full text | |
| Author(s): |
Total Authors: 2
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| Affiliation: | [1] Univ Estadual Campinas, Dept Math, BR-13083859 Campinas, SP - Brazil
[2] Univ Calif Riverside, Dept Math, Riverside, CA 92521 - USA
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | Journal of Algebra; v. 441, p. 216-242, NOV 1 2015. |
| Web of Science Citations: | 0 |
| Abstract | |
In this paper we study the category of graded modules for the current algebra associated to sl(2). The category enjoys many nice properties, including a tilting theory which was established in {[}1]. We show that the indecomposable tilting modules for sl(2){[}t] are the exterior powers of the fundamental global Weyl module and give the filtration multiplicities in the standard and costandard filtration. An interesting consequence of our result (which is far from obvious from the abstract definition) is that an indecomposable tilting module admits a free right action of the ring of symmetric polynomials in finitely many variables. Moreover, if we go modulo the augmentation ideal in this ring, the resulting sl(2){[}t]-module is isomorphic to the dual of a local Weyl module. (C) 2015 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 13/20243-5 - New directions in Lie Theory |
| Grantee: | Matthew Lyle Bennett |
| Support Opportunities: | Scholarships abroad - Research Internship - Post-doctor |
| FAPESP's process: | 12/06923-0 - On Filtrations and Homological Properties of Graded Modules for Current Algebras and Generalizations |
| Grantee: | Matthew Lyle Bennett |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |