Representations of Quantum Affinizations and Fusion Product
| dc.creator | Hernandez, David | |
| dc.date | 2003-12-17 | |
| dc.date | 2004-09-02 | |
| dc.date.accessioned | 2026-07-07T05:04:00Z | |
| dc.date.available | 2026-07-07T05:04:00Z | |
| dc.description | In this paper we study general quantum affinizations $\U_q(\hat{\Glie})$ of symmetrizable quantum Kac-Moody algebras and we develop their representation theory. We prove a triangular decomposition and we give a classication of (type 1) highest weight simple integrable representations analog to Drinfel'd-Chari-Pressley one. A generalization of the q-characters morphism, introduced by Frenkel-Reshetikhin for quantum affine algebras, appears to be a powerful tool for this investigation. For a large class of quantum affinizations (including quantum affine algebras and quantum toroidal algebras), the combinatorics of q-characters give a ring structure * on the Grothendieck group $\text{Rep}(\U_q(\hat{\Glie}))$ of the integrable representations that we classified. We propose a new construction of tensor products in a larger category by using the Drinfel'd new coproduct (it can not directly be used for $\text{Rep}(\U_q(\hat{\Glie}))$ because it involves infinite sums). In particular we prove that * is a fusion product (a product of representations is a representation). | |
| dc.description | 33 pages, 1 figure. Accepted for publication in Transformation Groups | |
| dc.identifier | https://arxiv.org/abs/math/0312336 | |
| dc.identifier | http://arxiv.org/abs/math/0312336 | |
| dc.identifier | Transformation Groups 10 (2005), no. 2, 163--200 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69635 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.title | Representations of Quantum Affinizations and Fusion Product | |
| dc.type | text |