PBW bases of irreducible Ising modules
| Autor: | Salazar, Diego |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Journal of Algebra Volume 639, 1 February 2024, Pages 398-421 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jalgebra.2023.10.015 |
| Popis: | 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 $\left(\begin{smallmatrix} 8 & 3 \\ 3 & 2 \end{smallmatrix}\right)$. Comment: 17 pages. Minor typographical errors were corrected and explanations were improved in the version published in the journal |
| Databáze: | arXiv |
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