dorsal/arxiv
View SchemaClassification of irreducible modules of W_3 algebra with c = -2
| Authors | Weiqiang Wang |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9708016 |
| URL | https://arxiv.org/abs/q-alg/9708016 |
| DOI | 10.1007/s002200050382 |
Abstract
We construct irreducible modules V_{\alpha}, \alpha \in \C over W_3 algebra with c = -2 in terms of a free bosonic field. We prove that these modules exhaust all the irreducible modules of W_3 algebra with c = -2. Highest weights of modules V_{\alpha}, \alpha \in \C with respect to the full (two-dimensional) Cartan subalgebra of W_3 algebra are (\alpha(\alpha -1)/2, \alpha(\alpha -1)(2\alpha -1)/6). They are parametrized by points (t, w) on a rational curve w^2 - t^2 (8t + 1)/9 = 0. Irreducible modules of vertex algebra W_{1+\infty} with c = -1 are also classified.
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"abstract": "We construct irreducible modules V_{\\alpha}, \\alpha \\in \\C over W_3 algebra\nwith c = -2 in terms of a free bosonic field. We prove that these modules\nexhaust all the irreducible modules of W_3 algebra with c = -2. Highest weights\nof modules V_{\\alpha}, \\alpha \\in \\C with respect to the full (two-dimensional)\nCartan subalgebra of W_3 algebra are (\\alpha(\\alpha -1)/2, \\alpha(\\alpha\n-1)(2\\alpha -1)/6). They are parametrized by points (t, w) on a rational curve\nw^2 - t^2 (8t + 1)/9 = 0. Irreducible modules of vertex algebra W_{1+\\infty}\nwith c = -1 are also classified.",
"arxiv_id": "q-alg/9708016",
"authors": [
"Weiqiang Wang"
],
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"q-alg",
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"doi": "10.1007/s002200050382",
"title": "Classification of irreducible modules of W_3 algebra with c = -2",
"url": "https://arxiv.org/abs/q-alg/9708016"
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