Monomials of q and q,t-characters for non simply-laced quantum affinizations
| dc.creator | Hernandez, David | |
| dc.date | 2004-04-08 | |
| dc.date | 2005-02-04 | |
| dc.date.accessioned | 2026-07-07T05:07:18Z | |
| dc.date.available | 2026-07-07T05:07:18Z | |
| dc.description | Nakajima introduced the morphism of q,t-characters for finite dimensional representation of simply-laced quantum affine algebras : it is a t-deformation of the Frenkel-Reshetikhin's morphism of q-characters (sum of monomials in infinite variables). In math.QA/0212257 we generalized the construction of q,t-characters for non simply-laced quantum affine algebras. First in this paper we prove a conjecture of math.QA/0212257 : the monomials of q and q,t-characters of standard representations are the same in non simply-laced cases (the simply-laced cases were treated by Nakajima) and the coefficients are non negative. In particular these q,t-characters can be considered as t-deformations of q-characters. In the proof we show that for quantum affine algebras of type A, B, C and quantum toroidal algebras of type A^{(1)} the l-weight spaces of fundamental representations are of dimension 1. Eventually we show and use a generalization of results of Frenkel-Reshetikhin, -Mukhin and Nakajima : for general quantum affinizations we prove that the l-weights of a l-highest weight simple module are lower than the highest l-weight in the sense of monomials. | |
| dc.description | 23 pages; accepted for publication in Mathematische Zeitschrift | |
| dc.identifier | https://arxiv.org/abs/math/0404187 | |
| dc.identifier | http://arxiv.org/abs/math/0404187 | |
| dc.identifier | Mathematische Zeitschrift 250 (2005), no. 2, 443--473 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70809 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Combinatorics | |
| dc.subject | Representation Theory | |
| dc.title | Monomials of q and q,t-characters for non simply-laced quantum affinizations | |
| dc.type | text |