Vertex algebraic structure of principal subspaces of basic \(A_{2n}^{(2)}\)-modules.(English)Zbl 1395.17059
Summary: We obtain a presentation of the principal subspace of the basic \(A_{2n}^{(2)}\)-module, \(n\geq 1\). We show that its full character is given by the Nahm sum of the tadpole Dynkin diagram \(T_n = A_{2n} / \mathbb{Z}_2\). This character is conjecturally modular after certain specializations. We prove the modularity property in the case of the affine Lie algebra of type \(A_4^{(2)}\).
MSC:
| 17B69 | Vertex operators; vertex operator algebras and related structures |
| 17B67 | Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras |
| 11P84 | Partition identities; identities of Rogers-Ramanujan type |
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