A half-twist type formula for the R-matrix of a symmetrizable Kac-Moody algebra
| dc.creator | Tingley, Peter | |
| dc.date | 2008-10-01 | |
| dc.date | 2008-10-06 | |
| dc.date.accessioned | 2026-07-07T10:07:23Z | |
| dc.date.available | 2026-07-07T10:07:23Z | |
| dc.description | Kirillov-Reshetikhin and Levendorskii-Soibelman developed a formula for the universal R-matrix of the form R=(X^{-1} \otimes X^{-1}) Δ(X). The action of X on a representation V permutes weight spaces according to the longest element in the Weyl group, so is only defined in finite type. We give a similar formula which is valid for the quantized universal enveloping algebra of any symmetrizable Kac-Moody algebra. This is done by replacing the action of X on V with an endomorphism that preserves weight spaces, but which is bar-linear instead of linear. | |
| dc.description | 9 pages. v2: minor corrections | |
| dc.identifier | https://arxiv.org/abs/0810.0088 | |
| dc.identifier | http://arxiv.org/abs/0810.0088 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170618 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.title | A half-twist type formula for the R-matrix of a symmetrizable Kac-Moody algebra | |
| dc.type | text |