Representations of Affine Quantum Function Algebras
| dc.creator | Narayanan, Bharath | |
| dc.date | 2002-12-08 | |
| dc.date.accessioned | 2026-07-07T04:53:37Z | |
| dc.date.available | 2026-07-07T04:53:37Z | |
| dc.description | Let $C$ be a symmetrizable generalized Cartan Matrix, and $q$ an indeterminate. ${\fg}(C)$ is the Kac-Moody Lie algebra and $U=U_q({\fg}(C))$ the associated quantum enveloping algebra over $ k={\Bbb Q}(q)$. The quantum function algebra ${\Bbb C}_{q}[G]$ is defined as a suitable $U$-bisubalgebra of the dual space $\hom_{k}(U,k)$ which can be described using matrix elements of integrable $U$-modules. For $\fg$ affine, the highest weight modules of $C_q[G]$ are constructed and, assuming a minimality condition, their (unitarizable) irreducible quotients are shown to be in a 1-1 correspondence with the reduced elements of the Weyl group of ${\frak g}(C)$. Further, these simple module are described in terms of the $C_q[SL_2]$-modules obtained by restriction, and they satisfy a Tensor Product theorem, similar to the finite type case. | |
| dc.description | 31 pages, adapted from PhD thesis, May 2002, KSU | |
| dc.identifier | https://arxiv.org/abs/math/0212112 | |
| dc.identifier | http://arxiv.org/abs/math/0212112 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65923 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.subject | 20G42 (Primary), 17B67, 81R50 (Secondary) | |
| dc.title | Representations of Affine Quantum Function Algebras | |
| dc.type | text |