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arXiv · 2306.11603

Semi-infinite construction of one-dimensional lattice vertex superalgebras

Timur Kenzhaev
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Abstract

We construct the Feigin-Stoyanovsky (combinatorial) basis in case of one-dimensional lattice vertex superalgebras $V_{\sqrt{N}\,\mathbb{Z}}$. Our proof is based on invariance of semi-infinite monomials linear span under action of corresponding Heisenberg algebra. Semi-infinite monomials are parametrized by natural generalization of Maya diagrams $\unicode{x2013}$ Fibonacci configurations on $\mathbb{Z}$, which allows us to construct a desired basis with character considerations. We also discuss some related questions such as functional realization of basic subspace's dual and representational proof of Feigin-Stoyanovsky construction in case of $V_{\sqrt{2}\,\mathbb{Z}}$.

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Timur Kenzhaev. 2023-06-20. Semi-infinite construction of one-dimensional lattice vertex superalgebras. https://arxiv.org/abs/2306.11603

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