Classification of irreducible unitary modules over $\mathfrak{u}(p,q|n)$
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908994830860288 |
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| author | Gould, Mark D. Pulemotov, Artem Rasmussen, Jorgen Zhang, Yang |
| author_facet | Gould, Mark D. Pulemotov, Artem Rasmussen, Jorgen Zhang, Yang |
| contents | We classify all irreducible highest-weight unitary modules over the non-compact real form $\mathfrak{u}(p,q|n)$ of the general linear Lie superalgebra $\mathfrak{gl}_{p+q|n}$. The classification is given by explicit necessary and sufficient conditions on the highest weights, and our approach combines the Howe duality for $\mathfrak{gl}_{p+q|n}$ with a quadratic invariant of the maximal compact subalgebra. Using this classification result, we also classify all irreducible lowest-weight unitary modules over $\mathfrak{u}(p,q|n)$ via duality, and all irreducible unitary modules over $\mathfrak{u}(n|q,p)$ via an isomorphism of Lie superalgebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28094 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classification of irreducible unitary modules over $\mathfrak{u}(p,q|n)$ Gould, Mark D. Pulemotov, Artem Rasmussen, Jorgen Zhang, Yang Representation Theory High Energy Physics - Theory Mathematical Physics We classify all irreducible highest-weight unitary modules over the non-compact real form $\mathfrak{u}(p,q|n)$ of the general linear Lie superalgebra $\mathfrak{gl}_{p+q|n}$. The classification is given by explicit necessary and sufficient conditions on the highest weights, and our approach combines the Howe duality for $\mathfrak{gl}_{p+q|n}$ with a quadratic invariant of the maximal compact subalgebra. Using this classification result, we also classify all irreducible lowest-weight unitary modules over $\mathfrak{u}(p,q|n)$ via duality, and all irreducible unitary modules over $\mathfrak{u}(n|q,p)$ via an isomorphism of Lie superalgebras. |
| title | Classification of irreducible unitary modules over $\mathfrak{u}(p,q|n)$ |
| topic | Representation Theory High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2603.28094 |