dorsal/arxiv
View SchemaVacuum curves of elliptic L-operators and representations of Sklyanin algebra
| Authors | I. Krichever, A. Zabrodin |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9801022 |
| URL | https://arxiv.org/abs/solv-int/9801022 |
Abstract
An algebro-geometric approach to representations of Sklyanin algebra is proposed. To each 2 \times 2 quantum L-operator an algebraic curve parametrizing its possible vacuum states is associated. This curve is called the vacuum curve of the L-operator. An explicit description of the vacuum curve for quantum L-operators of the integrable spin chain of XYZ type with arbitrary spin $\ell$ is given. The curve is highly reducible. For half-integer $\ell$ it splits into $\ell +{1/2}$ components isomorphic to an elliptic curve. For integer $\ell$ it splits into $\ell$ elliptic components and one rational component. The action of elements of the L-operator to functions on the vacuum curve leads to a new realization of the Sklyanin algebra by difference operators in two variables restricted to an invariant functional subspace.
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"abstract": "An algebro-geometric approach to representations of Sklyanin algebra is\nproposed. To each 2 \\times 2 quantum L-operator an algebraic curve\nparametrizing its possible vacuum states is associated. This curve is called\nthe vacuum curve of the L-operator. An explicit description of the vacuum curve\nfor quantum L-operators of the integrable spin chain of XYZ type with arbitrary\nspin $\\ell$ is given. The curve is highly reducible. For half-integer $\\ell$ it\nsplits into $\\ell +{1/2}$ components isomorphic to an elliptic curve. For\ninteger $\\ell$ it splits into $\\ell$ elliptic components and one rational\ncomponent. The action of elements of the L-operator to functions on the vacuum\ncurve leads to a new realization of the Sklyanin algebra by difference\noperators in two variables restricted to an invariant functional subspace.",
"arxiv_id": "solv-int/9801022",
"authors": [
"I. Krichever",
"A. Zabrodin"
],
"categories": [
"solv-int",
"hep-th",
"nlin.SI"
],
"title": "Vacuum curves of elliptic L-operators and representations of Sklyanin algebra",
"url": "https://arxiv.org/abs/solv-int/9801022"
},
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