Zero-level integrable modules over twisted affine Lie superalgebras
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911408479797248 |
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| author | Kiamehr, Hajar Rao, Senapathi Eswara Yousofzadeh, Malihe |
| author_facet | Kiamehr, Hajar Rao, Senapathi Eswara Yousofzadeh, Malihe |
| contents | The main result of this paper is the characterization of zero-level integrable finite weight modules, over twisted affine Lie superalgebras. We prove that such a module is parabolically induced from a module which is obtained, in a prescribed way, from a module over a Lie algebra $\mathscr{L}$ which is either a $\bbbz$-graded abelian Lie algebra or a direct sum of a $\bbbz$-graded abelian Lie algebra and the so-called quadratic Lie superalgebra $\mathcal{Q}$. We give also a complete characterization of both finite dimensional simple $\mathcal{Q}$-modules as well as bounded finite weight $\bbbz$-graded simple $\mathcal{Q}$-modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22210 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Zero-level integrable modules over twisted affine Lie superalgebras Kiamehr, Hajar Rao, Senapathi Eswara Yousofzadeh, Malihe Representation Theory The main result of this paper is the characterization of zero-level integrable finite weight modules, over twisted affine Lie superalgebras. We prove that such a module is parabolically induced from a module which is obtained, in a prescribed way, from a module over a Lie algebra $\mathscr{L}$ which is either a $\bbbz$-graded abelian Lie algebra or a direct sum of a $\bbbz$-graded abelian Lie algebra and the so-called quadratic Lie superalgebra $\mathcal{Q}$. We give also a complete characterization of both finite dimensional simple $\mathcal{Q}$-modules as well as bounded finite weight $\bbbz$-graded simple $\mathcal{Q}$-modules. |
| title | Zero-level integrable modules over twisted affine Lie superalgebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2601.22210 |