Generalized Umemura polynomials and Hirota-Miwa equations
| dc.creator | Kirillov, Anatol N. | |
| dc.creator | Taneda, Makoto | |
| dc.date | 2001-06-05 | |
| dc.date.accessioned | 2026-07-07T04:41:59Z | |
| dc.date.available | 2026-07-07T04:41:59Z | |
| dc.description | We introduce and study generalized Umemura polynomials $U_{n,m}^{(k)}(z,w;a,b)$ which are the natural generalization of the Umemura polynomials $U_n(z,w;a,b)$ related to the Painleve VI equation. We show that if either a=b, or a=0, or b=0, then polynomials $U_{n,m}^{(0)}(z,w;a,b)$ generate solutions to the Painleve VI equation. We give new proof of Noumi-Okada-Okamoto-Umemura conjecture, and describe connections between polynomials $U_{n,m}^{(0)}(z,w;a,0)$ and certain Umemura polynomials $U_k(z,w;α,β)$. Finally we show that after appropriate rescaling, Umemura's polynomials $U_k(z,w;a,b)$ satisfy the Hirota-Miwa bilinear equations. | |
| dc.description | 19 pages | |
| dc.identifier | https://arxiv.org/abs/math/0106025 | |
| dc.identifier | http://arxiv.org/abs/math/0106025 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61588 | |
| dc.subject | Combinatorics | |
| dc.subject | Quantum Algebra | |
| dc.subject | 14D15; 34M55 | |
| dc.title | Generalized Umemura polynomials and Hirota-Miwa equations | |
| dc.type | text |