Howe duality for the dual pair SL₂(\mathbb R) × F_4,1: a ping-pong of K-types

2025/08/17 by Savin, Gordan
#22E46 #22E47 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2508.12534

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.

Citations

• On the classification of unitary highest weight modules in the exceptional cases
• Howe duality and dichotomy for exceptional theta correspondences
• Global uniqueness of small representations

Related

• A Howe-type correspondence for the dual pair (sl(2),sl(n)) in sl(2n)
• The Howe duality conjecture: quaternionic case
• Similitude exceptional theta correspondences
• On the Howe duality conjecture in classical theta correspondence
• A proof of the Howe duality conjecture