Dihua Jiang, David Soudry
On the Genericity of Cuspidal Automorphic Forms of SO_{2n+1}
Preprint series: ESI preprints

MSC:

22E99 None of the above but in this section

11F99 None of the above but in this section

Abstract: We study the irreducible generic cuspidal support up to near equivalence for certain
cuspidal automorphic forms of $\SO_{2n+1}$ (Theorem 3.2 and Theorem 4.1), by establishing
refined arguments in the theory of local and global Howe duality and theta correspondences
(\cite{JngS03}, \cite{F95}) and in the theory of Langlands functoriality (\cite{CKPSS01},
\cite{JngS03}, \cite{GRS01}). The results support a global analogy and generalization of
a conjecture of Shahidi on the genericity of tempered local $L$-packets (Conjecture 1.1).
The methods are expected to work for other classical groups.