On the classification of unitary highest weight modules
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912194924380160 |
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| author | Pandžić, Pavle Prlić, Ana Souček, Vladimír Tuček, Vít |
| author_facet | Pandžić, Pavle Prlić, Ana Souček, Vladimír Tuček, Vít |
| contents | In the 1980s, Enright, Howe and Wallach [EHW] and independently Jakobsen [J] gave a complete classification of the unitary highest weight modules. In this paper we give a more direct and elementary proof of the same result for the (universal covers of the) Lie groups $Sp(2n, \mathbb{R}), SO^{*}(2n)$ and $SU(p, q)$. We also show how to describe the set of unitary highest weight modules with a given infinitesimal character. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_15892 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the classification of unitary highest weight modules Pandžić, Pavle Prlić, Ana Souček, Vladimír Tuček, Vít Representation Theory 22E47 In the 1980s, Enright, Howe and Wallach [EHW] and independently Jakobsen [J] gave a complete classification of the unitary highest weight modules. In this paper we give a more direct and elementary proof of the same result for the (universal covers of the) Lie groups $Sp(2n, \mathbb{R}), SO^{*}(2n)$ and $SU(p, q)$. We also show how to describe the set of unitary highest weight modules with a given infinitesimal character. |
| title | On the classification of unitary highest weight modules |
| topic | Representation Theory 22E47 |
| url | https://arxiv.org/abs/2305.15892 |