A family of Spin(8) dual pairs: the case of real groups

2023/02/05 by Wee Teck Gan, Hung Yean Loke, Gan, Wee Teck +5
Mathematics · #22E46 #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2302.02492

openalex publication_date 2023/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Exceptional groups of type E₆ contain dual pairs where one member is Spin(8), and the other is T\rtimes \mathbb Z/2\mathbb Z, where T is a two-dimensional torus and the non-trivial element in \mathbb Z/2\mathbb Z acts on T by the inverse involution. We describe the correspondence of representations arising by restricting the minimal representation.

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