4 problems

Let $\chi$ be an ${}^LG$-oper on $X$ with real monodromy, meaning that its monodromy representation is isomorphic to its complex conjugate. Then its monodromy is contained in an in…

Let $G$ be a real reductive group and let $\pi$ be an irreducible unitary representation of $G(\mathbb{C})$. Discrete-spectrum base-change conjecture. There is at most one pure inn…

Let $G$ be a reductive algebraic group over $\mathbb{R}$, and let $\pi$ be an irreducible representation of $G(\mathbb{C})$. Complex-real distinction conjecture. If…

Converse stability conjecture. If $(G,H,\theta)$ is p-stable, then $(G,H,\theta)$ is stable.