PreprintCC BY 4.0arXiv
Long-root SL2 dual pairs in split exceptional groups: Compact types, cone geometry, and theta correspondence
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.
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BibTeX
@misc{savin2026longroot,
title = {{Long-root $\SL_2$ dual pairs in split exceptional groups: Compact types, cone geometry, and theta correspondence}},
author = {Gordan Savin},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.08716},
eprint = {2611.08716},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.08716},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Long-root SL_2 dual pairs in split exceptional groups: Compact types, cone geometry, and theta correspondence
AU - Gordan Savin
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.08716
UR - https://arxiv.org/abs/2611.08716
AB - 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.
ER -