Norm of a Bethe Vector and the Hessian of the Master Function
| dc.creator | Mukhin, Evgeny | |
| dc.creator | Varchenko, Alexander | |
| dc.date | 2004-02-23 | |
| dc.date.accessioned | 2026-07-07T05:05:38Z | |
| dc.date.available | 2026-07-07T05:05:38Z | |
| dc.description | We show that the Bethe vectors are non-zero vectors in the sl_{r+1} Gaudin model. Moreover, we show that the norm of a Bethe vector is equal to the Hessian of the corresponding master function at the corresponding non-degenerate critical point. This result is a byproduct of functorial properties of Bethe vectors studied in this paper. As other byproducts of functoriality we show that the Bethe vectors form a basis in the tensor product of several copies of first and last fundamental sl_{r+1} modules and we show transversality of some Schubert cycles in the Grassmannian of r+1-dimensional planes in the space of polynomials of one variable of degree not greater than d. | |
| dc.description | Latex, 23 pages | |
| dc.identifier | https://arxiv.org/abs/math/0402349 | |
| dc.identifier | http://arxiv.org/abs/math/0402349 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70236 | |
| dc.subject | Quantum Algebra | |
| dc.title | Norm of a Bethe Vector and the Hessian of the Master Function | |
| dc.type | text |