Global Theta Liftings of General Linear Groups

J. Math. Sci. Univ. Tokyo
Vol. 3 (1996), No. 3, Page 699--711.

Watanabe, Takao
Global Theta Liftings of General Linear Groups
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A global theta lifting of some irreducible type 2 dual reductive pair is studied. It is proved that the image of a global theta lifting of a given irreducible automorphic cuspidal representation is nonvanishing if and only if its standard $L$-function is nonzero at the point $1/2$, and then the image coincides with the initial automorphic cuspidal representation. As a corollary of this result, the global Howe correspondence is obtained.

Mathematics Subject Classification (1991): Primary 11F70; Secondary 11F27, 22E50
Mathematical Reviews Number: MR1432113

Received: 1995-09-01