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1 results

  • Endoscopic lifts from PGL3 to G2

  • Wee Teck Gan, Gordan Savin
  • Journal:
    Compositio Mathematica / Volume 140 / Issue 3 / May 2004
    Published online by Cambridge University Press:
    04 December 2007, pp. 793-808
    Print publication:
    May 2004
    • Article
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  • 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.