A q-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra
| dc.creator | Hopkins, Mark J. | |
| dc.creator | Molev, Alexander I. | |
| dc.date | 2006-06-06 | |
| dc.date | 2006-12-26 | |
| dc.date.accessioned | 2026-07-07T09:34:32Z | |
| dc.date.available | 2026-07-07T09:34:32Z | |
| dc.description | We prove an analogue of the Sylvester theorem for the generator matrices of the quantum affine algebra ${\rm U}_q(\hat{\mathfrak{gl}}_n)$. We then use it to give an explicit realization of the skew representations of the quantum affine algebra. This allows one to identify them in a simple way by calculating their highest weight, Drinfeld polynomials and the Gelfand-Tsetlin character (or $q$-character). We also apply the quantum Sylvester theorem to construct a $q$-analogue of the Olshanski algebra as a projective limit of certain centralizers in ${\rm U}_q(\mathfrak{gl}_n)$ and show that this limit algebra contains the $q$-Yangian as a subalgebra. | |
| dc.description | This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/ | |
| dc.identifier | https://arxiv.org/abs/math/0606121 | |
| dc.identifier | http://arxiv.org/abs/math/0606121 | |
| dc.identifier | SIGMA 2 (2006), 092, 29 pages | |
| dc.identifier | doi:10.3842/SIGMA.2006.092 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159525 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.title | A q-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra | |
| dc.type | text |