On the classification of unitary highest weight modules in the exceptional cases
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912654870708224 |
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| author | Pandžić, Pavle Prlić, Ana Savin, Gordan Souček, Vladimír Tuček, Vít |
| author_facet | Pandžić, Pavle Prlić, Ana Savin, Gordan Souček, Vladimír Tuček, Vít |
| contents | In our previous paper, we gave a complete classification of the unitary highest weight modules for the universal covers of the Lie groups $Sp(2n, \mathbb{R}), SO^{*}(2n)$ and $SU(p, q)$, using the Dirac inequality and the so called PRV product. In this paper, we complete the classification of the unitary highest weight modules for the remaining cases; i.e., universal covers of the Lie groups $SO_{e}(2, n)$, $E_{6(-14)}$ and $E_{7(-25)}$. We also describe unitary highest weight modules with given infinitesimal characters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06317 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the classification of unitary highest weight modules in the exceptional cases Pandžić, Pavle Prlić, Ana Savin, Gordan Souček, Vladimír Tuček, Vít Representation Theory In our previous paper, we gave a complete classification of the unitary highest weight modules for the universal covers of the Lie groups $Sp(2n, \mathbb{R}), SO^{*}(2n)$ and $SU(p, q)$, using the Dirac inequality and the so called PRV product. In this paper, we complete the classification of the unitary highest weight modules for the remaining cases; i.e., universal covers of the Lie groups $SO_{e}(2, n)$, $E_{6(-14)}$ and $E_{7(-25)}$. We also describe unitary highest weight modules with given infinitesimal characters. |
| title | On the classification of unitary highest weight modules in the exceptional cases |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2412.06317 |