This research aims to establish Howe duality for an exceptional theta correspondence.
Proved Howe duality for the dual pair SL2(ℝ) and F4,1.
Explored K-types of corresponding representations.
Utilized a pair of see-saw identities for the analysis.
Established a relationship between K-types of corresponding representations.
Demonstrated that the theta correspondence satisfies Howe duality.
Showed the effectiveness of see-saw identities in proving these relations.
Abstract
We prove Howe duality for an exceptional theta correspondence.To that end, we relate the K -types of corresponding representations by exploiting a pair of see-saw identities.