The local converse theorem for SO(2n+1) and applications

By Dihua Jiang, D. Soudry. 2003

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In this paper we characterize irreducible generic representations of SO 2n+1 (k) (where k is a p-adic field) by means of twisted local gamma factors (the Local Converse Theorem). As applications, we prove that two irreducible generic cuspidal automorphic representations of SO 2n+1 (A) (where A is the ring of adeles of a number field) are equivalent if their local components are equivalent at almost all local places (the Rigidity Theorem); and prove the Local Langlands Reciprocity Conjecture for generic supercuspidal representations of SO 2n+1 (k).

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/025b46459d2387e846d7cf17e16aa4db826c70b4

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Functoriality for the classical groups (2004, methodology): “In [26] Jiang and Soudry were able to then use the descent method to show that in part (a) of the theorem the local functoriality taking πv to Πv is bijective and that the description of Πv given determines the image completely, that is, the lift is onto the set of Πv with these properties.”
A conjecture on Whittaker-Fourier coefficients of cusp forms (2013, result): “entation whose functorial lift is π1 ⊞··· ⊞πk is orthogonal to σin L2(G(F)\G(A)). (See [CKPSS04, Theorem 11.2].) In the case ofSO(2n+1)itwas proved thatσis irreducible (see [GRS01], which is based on [JS03]). It follows from the results of [JS07b] that σis irreducible in the case G = fSp n as well. ”