dorsal/arxiv
View SchemaDouble-loop algebras and the Fock space
| Authors | M. Varagnolo, E. Vasserot |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9612035 |
| URL | https://arxiv.org/abs/q-alg/9612035 |
Abstract
The fermionic Fock space admits two different actions of the quantized enveloping algebra of $\hat\sln$> The first one is a q-deformation of the well-known level-one representation of the affine Lie algebra and the second one is a new level-zero action arising from solvable lattices models. In this paper we prove that these two constructions can be glued together to get a representation of a new object: the toridal quantum group. This representation involves some difference operatorators. It is due to the fact that the specialization at q=1 of the toroidal algebra is isomorphic to the enveloping algebra of the universal central extension of a current algebra over a quantum torus.
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"abstract": "The fermionic Fock space admits two different actions of the quantized\nenveloping algebra of $\\hat\\sln$\u003e The first one is a q-deformation of the\nwell-known level-one representation of the affine Lie algebra and the second\none is a new level-zero action arising from solvable lattices models. In this\npaper we prove that these two constructions can be glued together to get a\nrepresentation of a new object: the toridal quantum group. This representation\ninvolves some difference operatorators. It is due to the fact that the\nspecialization at q=1 of the toroidal algebra is isomorphic to the enveloping\nalgebra of the universal central extension of a current algebra over a quantum\ntorus.",
"arxiv_id": "q-alg/9612035",
"authors": [
"M. Varagnolo",
"E. Vasserot"
],
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"q-alg",
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"title": "Double-loop algebras and the Fock space",
"url": "https://arxiv.org/abs/q-alg/9612035"
},
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