The Bruhat-Tits theory is a key ingredient in the construction of irreducible smooth representations of p-adic reductive groups. We describe generalizations to arbitrary such representations of ...several results recently obtained in the case of supercuspidal representations, in particular regarding the local Langlands correspondence and the internal structure of the L-packets.
We prove that the enhanced L-parameters with semisimple cuspidal support are those which are obtained via the (ordinary) Springer correspondence.
Let G be a connected reductive group over a non-archimedean field F of residual characteristic p. In the case where G splits over a tamely ramified extension of F and p does not divide the order of the Weyl group of G, we show that the enhanced L-parameters with semisimple cuspidal support correspond to irreducible smooth representations of G(F) with non-singular supercuspidal support via the local Langlands correspondence constructed by Kaletha, under the assumption that the latter satisfies certain expected properties of functorial nature. As a consequence, we obtain that every compound L-packet of G(F) contains at least one representation with non-singular supercuspidal support.
Following the method developed by Waldspurger and Beuzart-Plessis in their proof of the local Gan-Gross-Prasad conjecture, we prove a local trace formula for the Ginzburg-Rallis model. By applying ...this trace formula, we prove the multiplicity one theorem for the Ginzburg-Rallis model over the tempered Vogan L-packets. In some cases, we also prove the epsilon dichotomy conjecture which gives a relation between the multiplicity and the exterior cube epsilon factor. This is a sequel to another work of ours in which we proved the geometric side of the trace formula.
Soit $G$ l'ensemble des points rationnels d'un groupe algébrique réductif non connexe $p$-adique de caractéristique $0$. Soit $G^0$ la composante neutre de $G$. On suppose que $G/G^0$ est commutatif ...et fini$.$ Notre motivation pour cette note est de rejoindre le cas connexe d'un papier précédent, Bettaïeb, (2003). Autrement dit, de retrouver une analogue à notre classification des représentations irréductibles tempérées de $G,$ lorsque $G$ est connexe. C'est-à-dire que toute représentation irréductible tempérée de $G$ est irréductiblement induite d'une limite de série discrète d'un sous-groupe de Lévi cuspidal de $G.$
Let $R$ be a commutative ring, let $F$ be a locally compact non-archimedean field of finite residual field $k$ of characteristic $p$, and let $\mathbf{G}$ be a connected reductive $F$-group. We show ...that the pro-$p$-Iwahori Hecke $R$-algebra of $G=\mathbf{G}(F)$ admits a presentation similar to the Iwahori–Matsumoto presentation of the Iwahori Hecke algebra of a Chevalley group, and alcove walk bases satisfying Bernstein relations. This was previously known only for a $F$-split group $\mathbf{G}$.
Let
G
be the unramified unitary group in three variables defined over a
p
-adic field with
p
≠
2
. In this paper, we establish a theory of newforms for the Rankin–Selberg integral for
G
introduced by ...Gelbart and Piatetski-Shapiro. We describe
L
and
ε
-factors defined through zeta integrals in terms of newforms. We show that zeta integrals of newforms for generic representations attain
L
-factors. As a corollary, we get an explicit formula for
ε
-factors of generic representations.
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