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arXiv · 2306.07920

PBW bases of irreducible Ising modules

Diego Salazar
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Abstract

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 $\left(\begin{smallmatrix} 8 & 3 \\ 3 & 2 \end{smallmatrix}\right)$.

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BibTeXRIS

Diego Salazar. 2023-06-13. PBW bases of irreducible Ising modules. https://doi.org/10.1016/j.jalgebra.2023.10.015

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