Howe duality for the dual pair $\left(\text{SpO}(2n|1)\,, \mathfrak{osp}(2|2)\right)$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914368869892096 |
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| author | Lavicka, Roman Merino, Allan |
| author_facet | Lavicka, Roman Merino, Allan |
| contents | The goal of our work is to study the decomposition of the joint action of $\mathscr{G} = \text{SpO}(2n|1)$ and $\mathfrak{g}' = \mathfrak{osp}(2|2)$ on the supersymmetric algebra $\text{S} = \text{S}(\mathbb{C}^{2n|1} \otimes \mathbb{C}^{1|1})$. As proved by Merino and Salmasian, we have a one-to-one correspondence between irreducible representations of $\mathscr{G}$ and $\mathfrak{g}'$ appearing as subrepresentations of $\text{S}$. In this paper, we obtained an explicit description of the highest weights and joint highest weight vectors for the representations of $\mathscr{G}$ and $\mathfrak{g}'$ appearing in the duality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04075 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Howe duality for the dual pair $\left(\text{SpO}(2n|1)\,, \mathfrak{osp}(2|2)\right)$ Lavicka, Roman Merino, Allan Representation Theory Primary: 17B10, Secondary: 17B20 The goal of our work is to study the decomposition of the joint action of $\mathscr{G} = \text{SpO}(2n|1)$ and $\mathfrak{g}' = \mathfrak{osp}(2|2)$ on the supersymmetric algebra $\text{S} = \text{S}(\mathbb{C}^{2n|1} \otimes \mathbb{C}^{1|1})$. As proved by Merino and Salmasian, we have a one-to-one correspondence between irreducible representations of $\mathscr{G}$ and $\mathfrak{g}'$ appearing as subrepresentations of $\text{S}$. In this paper, we obtained an explicit description of the highest weights and joint highest weight vectors for the representations of $\mathscr{G}$ and $\mathfrak{g}'$ appearing in the duality. |
| title | Howe duality for the dual pair $\left(\text{SpO}(2n|1)\,, \mathfrak{osp}(2|2)\right)$ |
| topic | Representation Theory Primary: 17B10, Secondary: 17B20 |
| url | https://arxiv.org/abs/2506.04075 |