Critical points of functions, sl_2 representations, and Fuchsian differential equations with only univalued solutions
| dc.creator | Scherbak, I. | |
| dc.creator | Varchenko, A. | |
| dc.date | 2001-12-24 | |
| dc.date | 2003-01-27 | |
| dc.date.accessioned | 2026-07-07T04:45:30Z | |
| dc.date.available | 2026-07-07T04:45:30Z | |
| dc.description | Let a second order Fuchsian differential equation with only univalued solutions have finite singular points at z_1, ..., z_n with exponents (a_1,b_1), ..., (a_n,b_n). Let the exponents at infinity be (A,B). Then for fixed generic z_1,...,z_n, the number of such Fuchsian equations is equal to the multiplicity of the irreducible sl_2 representation of dimension |A-B| in the tensor product of irreducible sl_2 representations of dimensions |a_1-b_1|, >..., |a_n-b_n|. To show this we count the number of critical points of a suitable function which plays the crucial role in constructions of the hypergeometric solutions of the sl_2 KZ equation and of the Bethe vectors in the sl_2 Gaudin model. As a byproduct of this study we conclude that the Bethe vectors form a basis in the space of states for the sl_2 inhomogeneous Gaudin model. | |
| dc.description | The final version, to appear in MMJ | |
| dc.identifier | https://arxiv.org/abs/math/0112269 | |
| dc.identifier | http://arxiv.org/abs/math/0112269 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/62975 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Critical points of functions, sl_2 representations, and Fuchsian differential equations with only univalued solutions | |
| dc.type | text |