dorsal/arxiv
View SchemaRepresentations of Yangians with Gelfand-Zetlin Bases
| Authors | Maxim Nazarov, Vitaly Tarasov |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9502008 |
| URL | https://arxiv.org/abs/q-alg/9502008 |
| Journal | J. Reine Angew. Math. 496 (1998), 181-212 |
Abstract
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.
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"abstract": "We study certain family of finite-dimensional modules over the Yangian\n$Y(gl_N)$. The algebra $Y(gl_N)$ comes equipped with a distinguished maximal\ncommutative subalgebra $A(gl_n)$ generated by the centres of all algebras in\nthe chain $Y(gl_1)\\subset Y(gl_2)\\subset...\\subset Y(gl_N)$. We study the\nfinite-dimensional $Y(gl_N)$-modules with a semisimple action of the subalgebra\n$A(gl_N)$. We call these modules tame.\n We provide a characterization of irreducible tame modules in terms of their\nDrinfeld polynomials. We prove that every irreducible tame module splits into a\ntensor product of modules corresponding to the skew Young diagrams and some\none-dimensional module.\n The eigenbases of $A(gl_N)$ in irreducible tame modules are called\nGelfand-Zetlin bases. We provide explicit formulas for the action of the\nDrinfeld generators of the algebra $Y(gl_N)$ on the vectors of Gelfand-Zetlin\nbases.",
"arxiv_id": "q-alg/9502008",
"authors": [
"Maxim Nazarov",
"Vitaly Tarasov"
],
"categories": [
"q-alg",
"math.QA"
],
"journal_ref": "J. Reine Angew. Math. 496 (1998), 181-212",
"title": "Representations of Yangians with Gelfand-Zetlin Bases",
"url": "https://arxiv.org/abs/q-alg/9502008"
},
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