PreprintCC BY 4.0arXiv
SL3 dual pairs
Abstract
We study the exceptional theta correspondence for dual pairs of the form SL3× G inside p-adic groups of type En, n=6,7,8. We establish Howe duality for lifts of all Whittaker-generic unitarizable representations of SL3. Our dual pair is in a see-saw relationship with a dual pair of the form G2 × H such that G/H is a rank-two symmetric space. Using the theta correspondence for SL3 × G, we prove a multiplicity-one result for H-invariant functionals on representations of G.
Related
BibTeX
@misc{bakic2026dual,
title = {{$\SL_3$ dual pairs}},
author = {Petar Bakić and Wee Teck Gan and Gordan Savin},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30479},
eprint = {2610.30479},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30479},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - SL_3 dual pairs
AU - Petar Bakić
AU - Wee Teck Gan
AU - Gordan Savin
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30479
UR - https://arxiv.org/abs/2610.30479
AB - We study the exceptional theta correspondence for dual pairs of the form SL_3× G inside p-adic groups of type E_n, n=6,7,8. We establish Howe duality for lifts of all Whittaker-generic unitarizable representations of SL_3. Our dual pair is in a see-saw relationship with a dual pair of the form G_2 × H such that G/H is a rank-two symmetric space. Using the theta correspondence for SL_3 × G, we prove a multiplicity-one result for H-invariant functionals on representations of G.
ER -