$L$-Functoriality for Local Theta Correspondence of Supercuspidal Representations with Unipotent Reduction
Printed: Feb 2017
The preservation principle of local theta correspondences of reductive dual pairs over
a $p$-adic field predicts the existence of a sequence of irreducible supercuspidal
representations of classical groups.
have a conjecture
about the Langlands parameters for the sequence of supercuspidal representations.
In this paper we prove modified versions of their conjectures for the case of
supercuspidal representations with unipotent reduction.
local theta correspondence, supercuspidal representation, preservation principle, Langlands functoriality
22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05]
11F27 - Theta series; Weil representation; theta correspondences
20C33 - Representations of finite groups of Lie type