1. CJM 2016 (vol 69 pp. 186)
||$L$-Functoriality for Local Theta Correspondence of Supercuspidal Representations with Unipotent Reduction|
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.
Keywords:local theta correspondence, supercuspidal representation, preservation principle, Langlands functoriality
Categories:22E50, 11F27, 20C33
2. CJM 2008 (vol 60 pp. 1067)
||On Types for Unramified $p$-Adic Unitary Groups |
Let $F$ be a non-archimedean local field of residue characteristic
neither 2 nor 3 equipped with a galois involution with fixed field
$F_0$, and let $G$ be a symplectic group over $F$ or an unramified
unitary group over $F_0$. Following the methods of Bushnell--Kutzko for
$\GL(N,F)$, we define an analogue of a simple type attached to a
certain skew simple stratum, and realize a type in $G$. In
particular, we obtain an irreducible supercuspidal representation of
$G$ like $\GL(N,F)$.
Keywords:$p$-adic unitary group, type, supercuspidal representation, Hecke algebra