Orthogonal toroidal Lie algebras, vertex algebras and skew Howe duality. (English) Zbl 1497.17034
Summary: We generalize the skew Howe dualities \((\mathfrak{so}_{2 \nu} , O(\ell))\) and \((\mathfrak{so}_{2 \nu +1}, \mathrm{Pin}(\ell))\) to the toroidal Lie algebra and vertex algebra setups.
MSC:
| 17B67 | Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |
| 17B69 | Vertex operators; vertex operator algebras and related structures |
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