Two-parameter Quantum Group of Exceptional Type G_2 and Lusztig's Symmetries
| dc.creator | Hu, Naihong | |
| dc.creator | Shi, Qian | |
| dc.date | 2006-01-18 | |
| dc.date | 2007-04-05 | |
| dc.date.accessioned | 2026-07-07T07:56:56Z | |
| dc.date.available | 2026-07-07T07:56:56Z | |
| dc.description | We give the defining structure of two-parameter quantum group of type G_2 defined over a field {\Bbb Q}(r,s) (with r\ne s), and prove the Drinfel'd double structure as its upper and lower triangular parts, extending an earlier result of [BW1] in type A and a recent result of [BGH1] in types B, C, D. We further discuss the Lusztig's Q-isomorphisms from U_{r,s}(G_2) to its associated object U_{s^{-1},r^{-1}}(G_2), which give rise to the usual Lusztig's symmetries defined not only on U_q(G_2) but also on the centralized quantum group U_q^c(G_2) only when r=s^{-1}=q. (This also reflects the distinguishing difference between our newly defined two-parameter object and the standard Drinfel'd-Jimbo quantum groups). Some interesting (r,s)-identities holding in U_{r,s}(G_2) are derived from this discussion. | |
| dc.description | 34 pages. Pacific J. Math. (to appear in its simplified version) | |
| dc.identifier | https://arxiv.org/abs/math/0601444 | |
| dc.identifier | http://arxiv.org/abs/math/0601444 | |
| dc.identifier | Pacific Journal of Mathematics, vol. 230 (2), (2007), 327--346 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127499 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Representation Theory | |
| dc.subject | 17B37: 81R50; 17B35 | |
| dc.title | Two-parameter Quantum Group of Exceptional Type G_2 and Lusztig's Symmetries | |
| dc.type | text |