Representations of Yangians with Gelfand-Zetlin Bases
| dc.creator | Nazarov, Maxim | |
| dc.creator | Tarasov, Vitaly | |
| dc.date | 1995-02-13 | |
| dc.date | 2000-03-22 | |
| dc.date.accessioned | 2026-07-07T09:04:50Z | |
| dc.date.available | 2026-07-07T09:04:50Z | |
| dc.description | We study certain family of finite-dimensional modules over the Yangian $Y(gl_N)$. The algebra $Y(gl_N)$ comes equipped with a distinguished maximal commutative subalgebra $A(gl_n)$ generated by the centres of all algebras in the chain $Y(gl_1)\subset Y(gl_2)\subset...\subset Y(gl_N)$. We study the finite-dimensional $Y(gl_N)$-modules with a semisimple action of the subalgebra $A(gl_N)$. We call these modules tame. We provide a characterization of irreducible tame modules in terms of their Drinfeld polynomials. We prove that every irreducible tame module splits into a tensor product of modules corresponding to the skew Young diagrams and some one-dimensional module. The eigenbases of $A(gl_N)$ in irreducible tame modules are called Gelfand-Zetlin bases. We provide explicit formulas for the action of the Drinfeld generators of the algebra $Y(gl_N)$ on the vectors of Gelfand-Zetlin bases. | |
| dc.description | 30 pages, AmS-TeX, the final version | |
| dc.identifier | https://arxiv.org/abs/q-alg/9502008 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9502008 | |
| dc.identifier | J. Reine Angew. Math. 496 (1998), 181-212 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149522 | |
| dc.subject | Quantum Algebra | |
| dc.title | Representations of Yangians with Gelfand-Zetlin Bases | |
| dc.type | text |