The Hall algebra of a cyclic quiver and canonical bases of the Fock space
| dc.creator | Schiffmann, Olivier | |
| dc.date | 1999-06-11 | |
| dc.date | 1999-09-08 | |
| dc.date.accessioned | 2026-07-07T05:29:26Z | |
| dc.date.available | 2026-07-07T05:29:26Z | |
| dc.description | We prove that the Hall algebra U^-_n of the cyclic quiver of type A^(1)_{n-1} decomposes as a direct product of the quantum negative nilpotent subalgebra U_q^-(\hat{sl}_{n)) and C[q,q^{-1},z_1,z_2...]. We use this to prove a conjecture of Varagnolo and Vasserot in math/9803023 relating the canonical basis of U^-_n and the canonical basis of the level 1 Fock space representation of U_q(\hat{sl}_n) introduced by Leclerc and Thibon. This yields a proof of the positivity conjecture of Lascoux, Leclerc and Thibon, and a q-analogue of the Lusztig character formula for simple modules of the quantum group U_q(sl_n) at a root of unity. | |
| dc.description | Latex 2e, 22 pages, a section dealing with higher-level Fock spaces is added | |
| dc.identifier | https://arxiv.org/abs/math/9906069 | |
| dc.identifier | http://arxiv.org/abs/math/9906069 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78641 | |
| dc.subject | Quantum Algebra | |
| dc.title | The Hall algebra of a cyclic quiver and canonical bases of the Fock space | |
| dc.type | text |