Howe duality for the dual pair $S{L}_2(\mathbb{R})\times F_{4,1}$: a ping-pong of $K$-types

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.

6 pages

References in corpus (1)

• On the classification of unitary highest weight modules in the exceptional cases