Schumann, Bea (2017). Homological Description of Crystal Structures on Lusztig's Quiver Varieties. Int. Math. Res. Notices, 2017 (12). S. 3684 - 3726. OXFORD: OXFORD UNIV PRESS. ISSN 1687-0247
Full text not available from this repository.Abstract
Using methods of homological algebra, we obtain an explicit crystal isomorphism between two realizations of crystal bases of the lower part of the quantized enveloping algebra of (almost all) finite-dimensional simply laced Lie algebras. The first realization we consider is a geometric construction in terms of irreducible components of certain quiver varieties established by Kashiwara and Saito. The second is a realization in terms of isomorphism classes of quiver representations obtained by Reineke using Ringel's Hall algebra approach to quantum groups. We show that these two constructions are closely related by studying sufficiently generic representations of the preprojective algebra.
| Item Type: | Journal Article | ||||||||
| Creators: |
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| URN: | urn:nbn:de:hbz:38-228427 | ||||||||
| DOI: | 10.1093/imrn/rnw117 | ||||||||
| Journal or Publication Title: | Int. Math. Res. Notices | ||||||||
| Volume: | 2017 | ||||||||
| Number: | 12 | ||||||||
| Page Range: | S. 3684 - 3726 | ||||||||
| Date: | 2017 | ||||||||
| Publisher: | OXFORD UNIV PRESS | ||||||||
| Place of Publication: | OXFORD | ||||||||
| ISSN: | 1687-0247 | ||||||||
| Language: | English | ||||||||
| Faculty: | Unspecified | ||||||||
| Divisions: | Unspecified | ||||||||
| Subjects: | no entry | ||||||||
| Uncontrolled Keywords: |
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| Refereed: | Yes | ||||||||
| URI: | http://kups.ub.uni-koeln.de/id/eprint/22842 |
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