dorsal/arxiv
View SchemaWakimoto construction in the principal gradation
| Authors | A. H. Bougourzi |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9604020 |
| URL | https://arxiv.org/abs/q-alg/9604020 |
Abstract
It is well known that the bosonized version of the Wakimoto construction allows the explicit realization of any affine algebra $\widehat{g}$, with arbitrary level $k$ in the homogeneous gradation, in terms of $dim(g)$ free bosonic fields. In this paper, we show in the case of the simplest affine algebra $\widehat{sl(2)}$, that the bosonized Wakimoto realization can be extended to the principal gradation only when $k$ is equal to the critical level, i.e., -2. In this case, this construction can be achieved in terms of arbitrary number (larger than 1) of free bosonic fields.
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"date_created": "2026-03-02T18:01:28.467000Z",
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"abstract": "It is well known that the bosonized version of the Wakimoto construction\nallows the explicit realization of any affine algebra $\\widehat{g}$, with\narbitrary level $k$ in the homogeneous gradation, in terms of $dim(g)$ free\nbosonic fields. In this paper, we show in the case of the simplest affine\nalgebra $\\widehat{sl(2)}$, that the bosonized Wakimoto realization can be\nextended to the principal gradation only when $k$ is equal to the critical\nlevel, i.e., -2. In this case, this construction can be achieved in terms of\narbitrary number (larger than 1) of free bosonic fields.",
"arxiv_id": "q-alg/9604020",
"authors": [
"A. H. Bougourzi"
],
"categories": [
"q-alg",
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"title": "Wakimoto construction in the principal gradation",
"url": "https://arxiv.org/abs/q-alg/9604020"
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