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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.11603 |
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| _version_ | 1866914659773186048 |
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| author | Kenzhaev, Timur |
| author_facet | Kenzhaev, Timur |
| contents | 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 $V_{\sqrt{2}\,\mathbb{Z}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_11603 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Semi-infinite construction of one-dimensional lattice vertex superalgebras Kenzhaev, Timur Mathematical Physics 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 $V_{\sqrt{2}\,\mathbb{Z}}$. |
| title | Semi-infinite construction of one-dimensional lattice vertex superalgebras |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2306.11603 |