Endoscopic lifts from PGL3 to G2
Endoscopic lifts from PGL3 to G2
复制标题
内窥镜提升从 PGL3 到 G2
DOI：
10.1112/s0010437x03000678
复制
发表时间：
2004
影响因子：
1.8
通讯作者：
Gordan Savin
中科院分区：
文献类型：
--
作者：
W. Gan;Gordan Savin
我们本质上完全确定了p-ady域上的对偶${it pgl}_3\x G_2\子集E_6$所产生的theta对应。我们的第一个结果确定了PGL3的任何非超尖表示的提升力，并且表明提升力尊重朗兰兹函数。我们的第二个结果表明，PGL3的(非自对偶)超尖表示$\pi$的theta Lift$\pi$是G2的一个不可约通用超尖表示；当$\pi$有深度零时，我们也明确地确定了$\pi$。
We determine essentially completely the theta correspondence arising from the dual pair ${\it PGL}_3 \times G_2 \subset E_6$ over a p-adic field. Our first result determines the theta lift of any non-supercuspidal representation of PGL3 and shows that the lifting respects Langlands functoriality. Our second result shows that the theta lift $\theta(\pi)$ of a (non-self-dual) supercuspidal representation $\pi$ of PGL3 is an irreducible generic supercuspidal representation of G2; we also determine $\theta(\pi)$ explicitly when $\pi$ has depth zero.