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Search: All articles in the CJM digital archive with keyword endoscopy

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1. CJM Online first

Varma, Sandeep
On Residues of Intertwining Operators in Cases with Prehomogeneous Nilradical
Let $\operatorname{P} = \operatorname{M} \operatorname{N}$ be a Levi decomposition of a maximal parabolic subgroup of a connected reductive group $\operatorname{G}$ over a $p$-adic field $F$. Assume that there exists $w_0 \in \operatorname{G}(F)$ that normalizes $\operatorname{M}$ and conjugates $\operatorname{P}$ to an opposite parabolic subgroup. When $\operatorname{N}$ has a Zariski dense $\operatorname{Int} \operatorname{M}$-orbit, F. Shahidi and X. Yu describe a certain distribution $D$ on $\operatorname{M}(F)$ such that, for irreducible unitary supercuspidal representations $\pi$ of $\operatorname{M}(F)$ with $\pi \cong \pi \circ \operatorname{Int} w_0$, $\operatorname{Ind}_{\operatorname{P}(F)}^{\operatorname{G}(F)} \pi$ is irreducible if and only if $D(f) \neq 0$ for some pseudocoefficient $f$ of $\pi$. Since this irreducibility is conjecturally related to $\pi$ arising via transfer from certain twisted endoscopic groups of $\operatorname{M}$, it is of interest to realize $D$ as endoscopic transfer from a simpler distribution on a twisted endoscopic group $\operatorname{H}$ of $\operatorname{M}$. This has been done in many situations where $\operatorname{N}$ is abelian. Here, we handle the `standard examples' in cases where $\operatorname{N}$ is nonabelian but admits a Zariski dense $\operatorname{Int} \operatorname{M}$-orbit.

Keywords:induced representation, intertwining operator, endoscopy
Categories:22E50, 11F70

2. CJM Online first

Xu, Bin
On Moeglin's parametrization of Arthur packets for p-adic quasisplit $Sp(N)$ and $SO(N)$
We give a survey on Moeglin's construction of representations in the Arthur packets for $p$-adic quasisplit symplectic and orthogonal groups. The emphasis is on comparing Moeglin's parametrization of elements in the Arthur packets with that of Arthur.

Keywords:symplectic and orthogonal group, Arthur packet, endoscopy
Categories:22E50, 11F70

3. 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

4. CJM 2011 (vol 63 pp. 1083)

Kaletha, Tasho
Decomposition of Splitting Invariants in Split Real Groups
For a maximal torus in a quasi-split semi-simple simply-connected group over a local field of characteristic $0$, Langlands and Shelstad constructed a cohomological invariant called the splitting invariant, which is an important component of their endoscopic transfer factors. We study this invariant in the case of a split real group and prove a decomposition theorem which expresses this invariant for a general torus as a product of the corresponding invariants for simple tori. We also show how this reduction formula allows for the comparison of splitting invariants between different tori in the given real group.

Keywords:endoscopy, real lie group, splitting invariant, transfer factor
Categories:11F70, 22E47, 11S37, 11F72, 17B22

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