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arXiv · 2205.05271

Vertex algebraic construction of modules for twisted affine Lie algebras of type $A_{2l}^{(2)}$

Ryo Takenaka
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Abstract

Let $\tilde{\mathfrak{g}}$ be the affine Lie algebra of type $A_{2l}^{(2)}$. The integrable highest weight $\tilde{\mathfrak{g}}$-module $L(kΛ_0)$ called the standard $\tilde{\mathfrak{g}}$-module is realized by a tensor product of the twisted module $V_L^T$ for the lattice vertex operator algebra $V_L$. By using such vertex algebraic construction, we construct bases of the standard module, its principal subspace and the parafermionic space. As a consequence, we obtain their character formulas and settle the conjecture for vacuum modules stated in arXiv:math/0102113.

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Ryo Takenaka. 2022-05-11. Vertex algebraic construction of modules for twisted affine Lie algebras of type $A_{2l}^{(2)}$. https://arxiv.org/abs/2205.05271

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