Argument Shift Method and Gaudin Model
| dc.creator | Rybnikov, Leonid | |
| dc.date | 2006-06-15 | |
| dc.date | 2006-11-08 | |
| dc.date.accessioned | 2026-07-07T07:17:20Z | |
| dc.date.available | 2026-07-07T07:17:20Z | |
| dc.description | We construct a family of maximal commutative subalgebras in the tensor product of n copies of the universal enveloping algebra U(g) of a semisimple Lie algebra g. This family is parameterized by collections μ; z_1,...,z_n, where μ\in g^*, and z_1,...,z_n are pairwise distinct complex numbers. The construction presented here generalizes the famous construction of the higher Gaudin hamiltonians due to Feigin, Frenkel, and Reshetikhin. For n=1, our construction gives a quantization of the family of maximal Poisson-commutative subalgebras in S(g) obtained by the argument shift method. Next, we describe natural representations of commutative algebras of our family in tensor products of finite-dimensional g-modules as certain degenerations of the Gaudin model. In the case of g=sl_r we prove that our commutative subalgebras have simple spectrum in tensor products of finite-dimensional g-modules for generic μand z_i. This implies simplicity of spectrum in the "generic" sl_r Gaudin model. | |
| dc.description | 15 pages, references added | |
| dc.identifier | https://arxiv.org/abs/math/0606380 | |
| dc.identifier | http://arxiv.org/abs/math/0606380 | |
| dc.identifier | Func. Anal. Appl. 40 (2006), No 3, pp. 30--43 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/113906 | |
| dc.subject | Representation Theory | |
| dc.subject | Quantum Algebra | |
| dc.title | Argument Shift Method and Gaudin Model | |
| dc.type | text |