Classical freeness of orthosymplectic affine vertex superalgebras
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| Format: | Preprint |
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2022
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| _version_ | 1866911983109931008 |
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| author | Creutzig, Thomas Linshaw, Andrew R. Song, Bailin |
| author_facet | Creutzig, Thomas Linshaw, Andrew R. Song, Bailin |
| contents | The question of when a vertex algebra is a quantization of the arc space of its associated scheme has recently received a lot of attention in both the mathematics and physics literature. This property was first studied by Tomoyuki Arakawa and Anne Moreau [Lectures on $\mathcal{W}$-algebras, Australian Representation Theory Workshop 2016, University of Melbourne], and was given the name "classical freeness" by Jethro van Ekeren and Reimundo Heluani in their work on chiral homology [Comm. Math. Phys. 386 (2021), no. 1, 495-550]. Later, it was extended to vertex superalgebras by Hao Li [Eur. J. Math. 7 (2021), 1689-1728]. In this note, we prove the classical freeness of the simple affine vertex superalgebra $L_n(\mathfrak{osp}_{m|2r})$ for all positive integers $m,n,r$ satisfying $-\frac{m}{2} + r +n+1 > 0$. In particular, it holds for the rational vertex superalgebras $L_n(\mathfrak{osp}_{1|2r})$ for all positive integers $r,n$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2211_15032 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Classical freeness of orthosymplectic affine vertex superalgebras Creutzig, Thomas Linshaw, Andrew R. Song, Bailin Quantum Algebra High Energy Physics - Theory Representation Theory The question of when a vertex algebra is a quantization of the arc space of its associated scheme has recently received a lot of attention in both the mathematics and physics literature. This property was first studied by Tomoyuki Arakawa and Anne Moreau [Lectures on $\mathcal{W}$-algebras, Australian Representation Theory Workshop 2016, University of Melbourne], and was given the name "classical freeness" by Jethro van Ekeren and Reimundo Heluani in their work on chiral homology [Comm. Math. Phys. 386 (2021), no. 1, 495-550]. Later, it was extended to vertex superalgebras by Hao Li [Eur. J. Math. 7 (2021), 1689-1728]. In this note, we prove the classical freeness of the simple affine vertex superalgebra $L_n(\mathfrak{osp}_{m|2r})$ for all positive integers $m,n,r$ satisfying $-\frac{m}{2} + r +n+1 > 0$. In particular, it holds for the rational vertex superalgebras $L_n(\mathfrak{osp}_{1|2r})$ for all positive integers $r,n$. |
| title | Classical freeness of orthosymplectic affine vertex superalgebras |
| topic | Quantum Algebra High Energy Physics - Theory Representation Theory |
| url | https://arxiv.org/abs/2211.15032 |