Reduction and inverse-reduction functors I: standard $\mathsf{V^k}(\mathfrak{sl}_2)$-modules
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| Format: | Preprint |
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2026
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| _version_ | 1866916027771650048 |
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| author | Fasquel, Justine Fursman, Ethan Ridout, David |
| author_facet | Fasquel, Justine Fursman, Ethan Ridout, David |
| contents | Quantum hamiltonian reduction is a fundamental tool of conformal field theory and vertex algebra representation theory. It has traditionally been applied to study highest-weight modules. On the other hand, inverse quantum hamiltonian reduction lends itself to the study of fully relaxed highest-weight modules and their spectral flows, sometimes called the standard modules. This is the first of several papers that study the composition of reduction and inverse-reduction functors. A general formalism is presented and exemplified with the simplest example, thereby computing the action of reduction on the standard modules of the affine vertex-operator algebra associated with $\mathfrak{sl}_2$. The appearence of unbounded spectral sequences in this formalism may be of independent interest. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_19708 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Reduction and inverse-reduction functors I: standard $\mathsf{V^k}(\mathfrak{sl}_2)$-modules Fasquel, Justine Fursman, Ethan Ridout, David Quantum Algebra Mathematical Physics Representation Theory Primary 17B69, Secondary 81R10, 17B67, 17B10 Quantum hamiltonian reduction is a fundamental tool of conformal field theory and vertex algebra representation theory. It has traditionally been applied to study highest-weight modules. On the other hand, inverse quantum hamiltonian reduction lends itself to the study of fully relaxed highest-weight modules and their spectral flows, sometimes called the standard modules. This is the first of several papers that study the composition of reduction and inverse-reduction functors. A general formalism is presented and exemplified with the simplest example, thereby computing the action of reduction on the standard modules of the affine vertex-operator algebra associated with $\mathfrak{sl}_2$. The appearence of unbounded spectral sequences in this formalism may be of independent interest. |
| title | Reduction and inverse-reduction functors I: standard $\mathsf{V^k}(\mathfrak{sl}_2)$-modules |
| topic | Quantum Algebra Mathematical Physics Representation Theory Primary 17B69, Secondary 81R10, 17B67, 17B10 |
| url | https://arxiv.org/abs/2605.19708 |