On the structure of W-algebras in type A
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915212565676032 |
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| author | Creutzig, Thomas Fasquel, Justine Linshaw, Andrew R. Nakatsuka, Shigenori |
| author_facet | Creutzig, Thomas Fasquel, Justine Linshaw, Andrew R. Nakatsuka, Shigenori |
| contents | We formulate and prove examples of a conjecture which describes the W-algebras in type A as successive quantum Hamiltonian reductions of affine vertex algebras associated with several hook-type nilpotent orbits. This implies that the affine coset subalgebras of hook-type W-algebras are building blocks of the W-algebras in type A. In the rational case, it turns out that the building blocks for the simple quotients are provided by the minimal series of the regular W-algebras. In contrast, they are provided by singlet-type extensions of W-algebras at collapsing levels which are irrational. In the latter case, several new sporadic isomorphisms between different W-algebras are established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08212 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the structure of W-algebras in type A Creutzig, Thomas Fasquel, Justine Linshaw, Andrew R. Nakatsuka, Shigenori Representation Theory Mathematical Physics Quantum Algebra 17B69, 81R10 We formulate and prove examples of a conjecture which describes the W-algebras in type A as successive quantum Hamiltonian reductions of affine vertex algebras associated with several hook-type nilpotent orbits. This implies that the affine coset subalgebras of hook-type W-algebras are building blocks of the W-algebras in type A. In the rational case, it turns out that the building blocks for the simple quotients are provided by the minimal series of the regular W-algebras. In contrast, they are provided by singlet-type extensions of W-algebras at collapsing levels which are irrational. In the latter case, several new sporadic isomorphisms between different W-algebras are established. |
| title | On the structure of W-algebras in type A |
| topic | Representation Theory Mathematical Physics Quantum Algebra 17B69, 81R10 |
| url | https://arxiv.org/abs/2403.08212 |