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A Class of Supercuspidal Representations of $G_2(k)$ |
Canad. Math. Bull. 42(1999), 393-400
Published:1999-09-01
Printed: Sep 1999
Printed: Sep 1999
- Gordan Savin
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 |