Long-root $\SL_2$ dual pairs in split exceptional groups: Compact types, cone geometry, and theta correspondence

arXiv:2611.08716v1 Announce Type: new Abstract: The paper establishes a case of Howe duality for an exceptional theta correspondence using the ping-pong of types method. To that end, one needs to compute lifts of types of maximal compact subgroups. A brand new ingredient enters here: The graded module of the minimal representations is the coordinate ring of an affine cone whose projectivization is a Grassmannian. Via the filtered Nakayama lemma the problem of lifting types becomes a problem in algebraic geometry: compute certain linear sections of the Grassmannian.

You are being forwarded in 6s — stay on this page