Duality for spherical representations in exceptional theta\n correspondences

2017/05/19 by Hung Yean Loke, Loke, Hung Yean, Gordan Savin +1
Mathematics · #22E46 22E47 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1705.07145

openalex publication_date 2017/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the exceptional theta correspondence for real groups obtained by\nrestricting the minimal representation of the split exceptional group of the\ntype E_n, to a split dual pair where one member is the exceptional group of the\ntype G₂. We prove that the correspondence gives a bijection between spherical\nrepresentations if n=6,7, and a slightly weaker statement if n=8.\n

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