4 problems

Enhancement conjecture. An enhancement of the $L$-parameter $\varphi$ with an irreducible representation of its component group is the appropriate object to study.

Let $G$ be the reductive group under consideration, let $F$ be its local field, and let $\iota:\overline{\mathbb{Q}}_{\ell}\overset{\sim}{\to}\mathbb{C}$ be a field isomorphism. Le…

Gross-Prasad--Rallis conjecture. The parameter $phi$ is generic if and only if

Dual generic representation conjecture. One has