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# A Class of Supercuspidal Representations of $G_2(k)$

Published:1999-09-01
Printed: Sep 1999
• Gordan Savin
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## Abstract

Let $H$ be an exceptional, adjoint group of type $E_6$ and split rank 2, over a $p$-adic field $k$. In this article we discuss the restriction of the minimal representation of $H$ to a dual pair $\PD^{\times}\times G_2(k)$, where $D$ is a division algebra of dimension 9 over $k$. In particular, we discover an interesting class of supercuspidal representations of $G_2(k)$.
 MSC Classifications: 22E35 - Analysis on $p$-adic Lie groups 22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05] 11F70 - Representation-theoretic methods; automorphic representations over local and global fields