Decomposition numbers and canonical bases
| dc.creator | Leclerc, Bernard | |
| dc.date | 1999-02-01 | |
| dc.date.accessioned | 2026-07-07T05:27:44Z | |
| dc.date.available | 2026-07-07T05:27:44Z | |
| dc.description | We obtain some simple relations between decomposition numbers of quantized Schur algebras at an n-th root of unity (over a field of characteristic 0). These relations imply that every decomposition number for such an algebra occurs as a decomposition number for some Hecke algebra of type A. We prove similar relations between coefficients of the canonical basis of the q-deformed Fock space previously introduced in a joint work with Thibon. It follows that these coefficients can all be expressed in terms of those of the global crystal basis of the irreducible sub-representation generated by the vacuum vector. As a consequence, using works of Ariki and Varagnolo-Vasserot, it is possible to give a new proof of Lusztig's character formula for the simple U_v(sl_r)-modules at roots of unity, which does not involve representations of sl^_r of negative level. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/9902006 | |
| dc.identifier | http://arxiv.org/abs/math/9902006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/78032 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.subject | MSC 17B 20C | |
| dc.title | Decomposition numbers and canonical bases | |
| dc.type | text |