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On the tempered $L$-functions conjecture
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 135, Number 3, June 2013
- pp. 777-799
- 10.1353/ajm.2013.0026
- Article
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We give a general proof of Shahidi's tempered L-function conjecture, which has
previously been known in all but one case. One of the consequences is the standard
module conjecture for $p$-adic groups, which means that the Langlands quotient of a
standard module is generic if and only if the standard module is irreducible and the
inducing data generic. We have also included the result that every generic tempered
representation of a $p$-adic group is a sub-representation of a representation
parabolically induced from a generic supercuspidal representation with a non-negative
real central character.