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Howe duality for the
dual pair $\mathrm{SL}_2(\mathbb{R}) \times F_{4,1}$: a ping
pong of $K$-types
Gordan Savin |
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Vol. 342 (2026), No. 2, 387–394
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Abstract |
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We prove Howe duality for an exceptional theta correspondence. To that end, we relate the -types of corresponding representations by exploiting a pair of see-saw identities. |
Keywords
minimal representation, theta correspondence
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Mathematical Subject Classification
Primary: 22E46, 22E47
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Milestones
Received: 4 December 2025
Revised: 8 January 2026
Accepted: 13 January 2026
Published: 23 April 2026
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Authors |
| Gordan Savin | |
| Department of Mathematics University of Utah Salt Lake City, UT United States |
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| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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