Applications of Langlands' functorial lift of odd orthogonal groups

Author:
Henry H. Kim

Journal:
Trans. Amer. Math. Soc. **354** (2002), 2775-2796

MSC (2000):
Primary 22E55, 11F70

DOI:
https://doi.org/10.1090/S0002-9947-02-02969-0

Published electronically:
March 6, 2002

MathSciNet review:
1895203

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Abstract: Together with Cogdell, Piatetski-Shapiro and Shahidi, we proved earlier the existence of a weak functorial lift of a generic cuspidal representation of to . Recently, Ginzburg, Rallis and Soudry obtained a more precise form of the lift using their integral representation technique, namely, the lift is an isobaric sum of cuspidal representations of (more precisely, cuspidal representations of such that the exterior square -functions have a pole at ). One purpose of this paper is to give a simpler proof of this fact in the case that a cuspidal representation has one supercuspidal component. In a separate paper, we prove it without any condition using a result on spherical unitary dual due to Barbasch and Moy. We give several applications of the functorial lift: First, we parametrize square integrable representations with generic supercuspidal support, which have been classified by Moeglin and Tadic. Second, we give a criterion for cuspidal reducibility of supercuspidal representations of . Third, we obtain a functorial lift from generic cuspidal representations of to automorphic representations of , corresponding to the -group homomorphism , given by the second fundamental weight.

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Additional Information

**Henry H. Kim**

Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON M5S 3G3, Canada

Email:
henrykim@math.toronto.edu

DOI:
https://doi.org/10.1090/S0002-9947-02-02969-0

Received by editor(s):
September 25, 2000

Received by editor(s) in revised form:
February 21, 2001, and September 27, 2001

Published electronically:
March 6, 2002

Additional Notes:
Partially supported by NSF grant DMS9988672, NSF grant DMS9729992 (at IAS) and by Clay Mathematics Institute.

Article copyright:
© Copyright 2002
American Mathematical Society