Howe duality for the dual pair $SL_2(\mathbb R) \times F_{4,1}$: a ping-pong of $K$-types
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914514067259392 |
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| author | Savin, Gordan |
| author_facet | Savin, Gordan |
| contents | We prove Howe duality for an exceptional theta correspondence. To that end we exploit a pair of see-saw identities and relate the $K$-types of corresponding representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12534 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Howe duality for the dual pair $SL_2(\mathbb R) \times F_{4,1}$: a ping-pong of $K$-types Savin, Gordan Representation Theory Number Theory 22E46, 22E47 We prove Howe duality for an exceptional theta correspondence. To that end we exploit a pair of see-saw identities and relate the $K$-types of corresponding representations. |
| title | Howe duality for the dual pair $SL_2(\mathbb R) \times F_{4,1}$: a ping-pong of $K$-types |
| topic | Representation Theory Number Theory 22E46, 22E47 |
| url | https://arxiv.org/abs/2508.12534 |