On Bethe vectors in the sl_{N+1} Gaudin model
| dc.creator | Chmutov, S. | |
| dc.creator | Scherbak, I. | |
| dc.date | 2004-07-22 | |
| dc.date | 2005-05-25 | |
| dc.date.accessioned | 2026-07-07T05:10:33Z | |
| dc.date.available | 2026-07-07T05:10:33Z | |
| dc.description | The note deals with the Gaudin model associated with the tensor product of n irreducible finite-dimensional sl_{N+1}-modules marked by distinct complex numbers z_1,..., z_n. The Bethe Ansatz is a method to construct common eigenvectors of the Gaudin hamiltonians by means of chosen singular vectors in the factors and z_j's. These vectors are called Bethe vectors. The question if the Bethe vectors are non-zero vectors is open. By the moment, the only way to verify that was based on a relation to critical points of the master function of the Gaudin model, and non-triviality of a Bethe vector was proved only in the case when the corresponding critical point is non-degenerate ([ScV], [MV1]). However degenerate critical points do appear in the Gaudin model (see Section12 of [ReV]). We believe that the Bethe vectors never vanish, and suggest an approach that does not depend on non-degeneracy of the corresponding critical point. The idea is for a Bethe vector to choose a suitable subspace in the weight space and to check that the projection of the Bethe vector to this subspace is non-zero. We apply this approach to verify non-triviality of Bethe vectors in new examples. | |
| dc.description | the final version, to appear in the IMRN | |
| dc.identifier | https://arxiv.org/abs/math/0407367 | |
| dc.identifier | http://arxiv.org/abs/math/0407367 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71960 | |
| dc.subject | Representation Theory | |
| dc.subject | Mathematical Physics | |
| dc.title | On Bethe vectors in the sl_{N+1} Gaudin model | |
| dc.type | text |