ﻻ يوجد ملخص باللغة العربية
In this paper we prove the Aubert-Baum-Plymen-Solleveld conjecture for the split classical groups and establish the connection with the Langlands correspondence. To do this, we review the notion of cuspidality for enhanced Langlands parameters and also review the notion of cuspidal support for enhanced Langlands parameters for split classical groups, both introduced by the author in earlier work.
Through combining the work of Jean-Loup Waldspurger (cite{waldspurger10} and cite{waldspurgertemperedggp}) and Raphael Beuzart-Plessis (cite{beuzart2015local}), we give a proof for the tempered part of the local Gan-Gross-Prasad conjecture (cite{ggpo
The formal degree conjecture and the root number conjecture are verified with respect to supercuspidal representations of $Sp_{2n}(F)$ and $L$-parameters associated with tamely ramified extension $K/F$ of degree $2n$. The supercuspidal representation
We present a proof of the compositional shuffle conjecture, which generalizes the famous shuffle conjecture for the character of the diagonal coinvariant algebra. We first formulate the combinatorial side of the conjecture in terms of certain operato
The main purpose of this paper is to prove a group-theoretic generalization of a theorem of Katz on isocrystals. Along the way we reprove the group-theoretic generalization of Mazurs inequality for isocrystals due to Rapoport-Richartz, and generalize
We stabilize the full Arthur-Selberg trace formula for the metaplectic covering of symplectic groups over a number field. This provides a decomposition of the invariant trace formula for metaplectic groups, which encodes information about the genuine