Bispectral and $(\glN,\glM)$ Dualities
| dc.creator | Mukhin, E. | |
| dc.creator | Tarasov, V. | |
| dc.creator | Varchenko, A. | |
| dc.date | 2005-10-18 | |
| dc.date.accessioned | 2026-07-07T06:47:35Z | |
| dc.date.available | 2026-07-07T06:47:35Z | |
| dc.description | Let $V = < p_{ij}(x)e^{\la_ix}, i=1,...,n, j=1, ..., N_i >$ be a space of quasi-polynomials of dimension $N=N_1+...+N_n$. Define the regularized fundamental operator of $V$ as the polynomial differential operator $D = \sum_{i=0}^N A_{N-i}(x)\p^i$ annihilating $V$ and such that its leading coefficient $A_0$ is a polynomial of the minimal possible degree. We construct a space of quasi-polynomials $U = < q_{ab}(u)e^{z_au} >$ whose regularized fundamental operator is the differential operator $\sum_{i=0}^N u^i A_{N-i}(\partial_u)$. The space $U$ is constructed from $V$ by a suitable integral transform. Our integral transform corresponds to the bispectral involution on the space of rational solutions (vanishing at infinity) to the KP hierarchy, see \cite{W}. As a corollary of the properties of the integral transform we obtain a correspondence between critical points of the two master functions associated with the $(\glN,\glM)$ dual Gaudin models as well as between the corresponding Bethe vectors. | |
| dc.identifier | https://arxiv.org/abs/math/0510364 | |
| dc.identifier | http://arxiv.org/abs/math/0510364 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103702 | |
| dc.subject | Quantum Algebra | |
| dc.title | Bispectral and $(\glN,\glM)$ Dualities | |
| dc.type | text |