CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Publicationsjournals
Publications        
Search results

Search: MSC category 11F27 ( Theta series; Weil representation; theta correspondences )

  Expand all        Collapse all Results 1 - 5 of 5

1. CJM Online first

Pan, Shu-Yen
$L$-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. Adams/Harris-Kudla-Sweet 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 2012 (vol 64 pp. 497)

Li, Wen-Wei
Le lemme fondamental pondéré pour le groupe métaplectique
Dans cet article, on énonce une variante du lemme fondamental pondéré d'Arthur pour le groupe métaplectique de Weil, qui sera un ingrédient indispensable de la stabilisation de la formule des traces. Pour un corps de caractéristique résiduelle suffisamment grande, on en donne une démonstration à l'aide de la méthode de descente, qui est conditionnelle: on admet le lemme fondamental pondéré non standard sur les algèbres de Lie. Vu les travaux de Chaudouard et Laumon, on s'attend à ce que cette condition soit ultérieurement vérifiée.

Keywords:fundamental lemma, metaplectic group, endoscopy, trace formula
Categories:11F70, 11F27, 22E50

3. CJM 2000 (vol 52 pp. 737)

Gan, Wee Teck
An Automorphic Theta Module for Quaternionic Exceptional Groups
We construct an automorphic realization of the global minimal representation of quaternionic exceptional groups, using the theory of Eisenstein series, and use this for the study of theta correspondences.

Categories:11F27, 11F70

4. CJM 1999 (vol 51 pp. 164)

Tan, Victor
Poles of Siegel Eisenstein Series on $U(n,n)$
Let $U(n,n)$ be the rank $n$ quasi-split unitary group over a number field. We show that the normalized Siegel Eisenstein series of $U(n,n)$ has at most simple poles at the integers or half integers in certain strip of the complex plane.

Categories:11F70, 11F27, 22E50

5. CJM 1998 (vol 50 pp. 1105)

Roberts, Brooks
Tempered representations and the theta correspondence
Let $V$ be an even dimensional nondegenerate symmetric bilinear space over a nonarchimedean local field $F$ of characteristic zero, and let $n$ be a nonnegative integer. Suppose that $\sigma \in \Irr \bigl(\OO (V)\bigr)$ and $\pi \in \Irr \bigl(\Sp (n,F)\bigr)$ correspond under the theta correspondence. Assuming that $\sigma$ is tempered, we investigate the problem of determining the Langlands quotient data for $\pi$.

Categories:11F27, 22E50

© Canadian Mathematical Society, 2016 : https://cms.math.ca/