dorsal/arxiv
View SchemaQuantum Affine Algebras and Deformations of the Virasoro and W-algebras
| Authors | Edward Frenkel, Nikolai Reshetikhin |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9505025 |
| URL | https://arxiv.org/abs/q-alg/9505025 |
| DOI | 10.1007/BF02104917 |
Abstract
We generalize some results concerning affine algebras at the critical level to the corresponding quantum algebras. In particular, we show that the Wakimoto realization provides a homomorphism of Poisson algebras from the center of a quantum affine algebra to a Heisenberg-Poisson algebra. This homomorphism is a q-deformation of the Miura transformation. It is given by the same formulas as the spectra of transfer-matrices of the corresponding quantum integrable models. The image of the center in the Heisenberg-Poisson algebra is a Poisson subalgebra of the latter, which is a q-deformation of the corresponding classical W-algebra. The relations in this Poisson algebra are explicitly computed in the case of sl(n)^.
{
"annotation_id": "77abe805-cec6-417a-84a5-dbe12332af7b",
"date_created": "2026-03-02T18:01:24.454000Z",
"date_modified": "2026-03-02T18:01:24.454000Z",
"file_hash": "2e6eec08bf847ef597b4b4dbbdd7b8f6146e1346d3353547bcbba1abc35a406b",
"private": false,
"record": {
"abstract": "We generalize some results concerning affine algebras at the critical level\nto the corresponding quantum algebras. In particular, we show that the Wakimoto\nrealization provides a homomorphism of Poisson algebras from the center of a\nquantum affine algebra to a Heisenberg-Poisson algebra. This homomorphism is a\nq-deformation of the Miura transformation. It is given by the same formulas as\nthe spectra of transfer-matrices of the corresponding quantum integrable\nmodels. The image of the center in the Heisenberg-Poisson algebra is a Poisson\nsubalgebra of the latter, which is a q-deformation of the corresponding\nclassical W-algebra. The relations in this Poisson algebra are explicitly\ncomputed in the case of sl(n)^.",
"arxiv_id": "q-alg/9505025",
"authors": [
"Edward Frenkel",
"Nikolai Reshetikhin"
],
"categories": [
"q-alg",
"hep-th",
"math.QA"
],
"doi": "10.1007/BF02104917",
"title": "Quantum Affine Algebras and Deformations of the Virasoro and W-algebras",
"url": "https://arxiv.org/abs/q-alg/9505025"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "ace87d9d-ec2d-4bac-9dda-fe580b6a23b4",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}