Demonstrates how $K$-types relate under Howe duality for the pair of groups.
Proves the exceptional theta correspondence through advanced pair of identities.
Utilizes see-saw identities to understand the representation connections.
Findings suggest deeper insights into representation theory and dual pairs.
Abstract
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.