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Exceptional groups of type \(E_6\) contain dual pairs where one member is \(\mathrm {Spin}(8)\) , and the other is \(T\rtimes \mathbb Z/2\mathbb Z\) , where T is a two-dimensional torus and the nontrivial 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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A Family of Spin(Eight) Dual Pairs: The Case of Real Groups

  • 章节

  • 发表日期：

    2025年

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  • Wee Teck Gan,
  • Hung Yean Loke,
  • Annegret Paul,
  • Gordan Savin

摘要

Exceptional groups of type \(E_6\) contain dual pairs where one member is \(\mathrm {Spin}(8)\) , and the other is \(T\rtimes \mathbb Z/2\mathbb Z\) , where T is a two-dimensional torus and the nontrivial 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.