Classification of irreducible modules for Bershadsky-Polyakov algebra at certain levels
| Autor: | Adamovic, Drazen, Kontrec, Ana |
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| Rok vydání: | 2019 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We study the representation theory of the Bershadsky-Polyakov algebra $\mathcal W_k = \mathcal{W}_k(sl_3,f_{\theta})$. In particular, Zhu algebra of $\mathcal W_k$ is isomorphic to a certain quotient of the Smith algebra, after changing the Virasoro vector. We classify all modules in the category $\mathcal{O}$ for the Bershadsky-Polyakov algebra $\mathcal W_k$ when $k=-5/3, -9/4, -1,0$. In the case $k=0$ we show that the Zhu algebra $A(\mathcal W_k)$ has $2$--dimensional indecomposable modules. Comment: Latex, 33 pages |
| Databáze: | arXiv |
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