The extended Weyl group $\widetilde{W}(D_5^{(1)})$ as an extension of KNY's birational representation of $\widetilde{W}(A_1^{(1)}\times A_3^{(1)})$
| dc.creator | Takenawa, Tomoyuki | |
| dc.date | 2002-03-14 | |
| dc.date | 2002-05-10 | |
| dc.date.accessioned | 2026-07-07T05:33:58Z | |
| dc.date.available | 2026-07-07T05:33:58Z | |
| dc.description | We study the birational representation of $\wt{W}(A_1^{(1)}\times A_3^{(1)})$ proposed by Kajiwara-Noumi-Yamada (KNY) in the case of $m=2$ and $n=4$. It is shown that the equation can be lifted to an automorphism of a family of $A_3^{(1)}$ surfaces and therefore the group of Cremona isometries is $\wt{W}(D_5^{(1)})$ ($\supset \wt{W}(A_1^{(1)}\times A_3^{(1)})$). The equation can be decomposed into two mappings which are conjugate to the $q$-$P_{VI}$ equation. It is also shown that the subgroup of Cremona isometries which commute with the original translation is isomorphic to $\mz \times \wt{W}(A_3^{(1)}) \times \wt{W}(A_1^{(1)})$. | |
| dc.description | 13 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/nlin/0203029 | |
| dc.identifier | http://arxiv.org/abs/nlin/0203029 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/80192 | |
| dc.subject | Exactly Solvable and Integrable Systems | |
| dc.title | The extended Weyl group $\widetilde{W}(D_5^{(1)})$ as an extension of KNY's birational representation of $\widetilde{W}(A_1^{(1)}\times A_3^{(1)})$ | |
| dc.type | text |