A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2006
• Main Authors: Hopkins, M.J., Molev, A.I.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2006
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/146061
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: A q-analogue of the centralizer construction and skew representations of the quantum Affine algebra / M.J. Hopkins, A.I. Molev // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 30 назв. — англ.

We prove an analogue of the Sylvester theorem for the generator matrices of the quantum affine algebra Uq(gln). 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 weig...