PBW bases of irreducible Ising modules
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866918468533616640 |
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| author | Salazar, Diego |
| author_facet | Salazar, Diego |
| contents | To every $h + \mathbb{N}$-graded module $M$ over an $\mathbb{N}$-graded conformal vertex algebra $V$, we associate an increasing filtration $(G^pM)_{p \in \mathbb{Z}}$ which is compatible with the filtrations introduced by Haisheng Li. The associated graded vector space $\mathrm{gr}^G(M)$ is naturally a module over the vertex Poisson algebra $\mathrm{gr}^G(V)$. We study $\mathrm{gr}^G(M)$ for the three irreducible modules of the Ising model $\mathrm{Vir}_{3, 4}$, namely $\mathrm{Vir}_{3,4} = L(1/2, 0)$, $L(1/2, 1/2)$ and $L(1/2, 1/16)$. We obtain an explicit monomial basis of each of these modules and a formula for their refined characters which are related to Nahm sums for the matrix $\left(\begin{smallmatrix} 8 & 3 \\ 3 & 2 \end{smallmatrix}\right)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_07920 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | PBW bases of irreducible Ising modules Salazar, Diego Quantum Algebra Combinatorics 17B69, 11P84 To every $h + \mathbb{N}$-graded module $M$ over an $\mathbb{N}$-graded conformal vertex algebra $V$, we associate an increasing filtration $(G^pM)_{p \in \mathbb{Z}}$ which is compatible with the filtrations introduced by Haisheng Li. The associated graded vector space $\mathrm{gr}^G(M)$ is naturally a module over the vertex Poisson algebra $\mathrm{gr}^G(V)$. We study $\mathrm{gr}^G(M)$ for the three irreducible modules of the Ising model $\mathrm{Vir}_{3, 4}$, namely $\mathrm{Vir}_{3,4} = L(1/2, 0)$, $L(1/2, 1/2)$ and $L(1/2, 1/16)$. We obtain an explicit monomial basis of each of these modules and a formula for their refined characters which are related to Nahm sums for the matrix $\left(\begin{smallmatrix} 8 & 3 \\ 3 & 2 \end{smallmatrix}\right)$. |
| title | PBW bases of irreducible Ising modules |
| topic | Quantum Algebra Combinatorics 17B69, 11P84 |
| url | https://arxiv.org/abs/2306.07920 |