Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Duality for spherical representations in exceptional theta correspondences


Authors: Hung Yean Loke and Gordan Savin
Journal: Trans. Amer. Math. Soc. 371 (2019), 6359-6375
MSC (2010): Primary 11F27, 22E46
DOI: https://doi.org/10.1090/tran/7471
Published electronically: August 24, 2018
MathSciNet review: 3937328
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study the exceptional theta correspondence for real groups obtained by restricting the minimal representation of the split exceptional group of the type $ \mathbf E_n$, to a split dual pair where one member is the exceptional group of the type $ \mathbf {G}_2$. We prove that the correspondence gives a bijection between spherical representations if $ n=6,7$, and a slightly weaker statement if $ n=8$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 11F27, 22E46

Retrieve articles in all journals with MSC (2010): 11F27, 22E46


Additional Information

Hung Yean Loke
Affiliation: Department of Mathematics, National University of Singapore, 21 Lower Kent Ridge Road, Singapore 119077
Email: matlhy@nus.edu.sg

Gordan Savin
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Email: savin@math.utah.edu

DOI: https://doi.org/10.1090/tran/7471
Received by editor(s): July 30, 2017
Received by editor(s) in revised form: November 24, 2017
Published electronically: August 24, 2018
Additional Notes: The first author was supported in part by an MOE-NUS AcRF Tier 1 grant R-146-000-208-112.
The second author was supported in part by an NSF grant DMS-1359774.
Article copyright: © Copyright 2018 American Mathematical Society