7 problems

In the setting of Theorem, let $G^{\Gamma}$ be an extended real reductive group, let $\psi$ be an Arthur parameter, and let the notation $\Pi^z(G^{\Gamma})^{mic}_{\psi}$ and…

Let $U(p,q)$ be the real reductive group of unitary matrices of signature $(p,q)$, and let $A_\mathfrak{q}(\lambda)$ denote a cohomologically induced module in the weakly fair rang…

Vogan's fundamental parallelepiped conjecture. If $X$ is unitary, then

Let $G$ be a real reductive group with Lie algebra $\mathfrak{g}$ and maximal compact subgroup $K$, and let $\pi$ be an irreducible unitary $(\mathfrak{g},K)$ module with infinites…

Cohomological-building-block conjecture. There exist a $\theta$-stable parabolic $\mathfrak{q}=\mathfrak{l}\oplus\mathfrak{u}$ such that

Let $A_{p,q}(k)$ denote a middle-dimensional cohomologically induced representation associated with a Levi subgroup $\widetilde{U}(p,q)$ of $Mp_{2n}(\mathbb R)$ or with a Levi subg…

Let $\mathfrak{g}$ be a finite-dimensional Lie algebra, let $\mathfrak{k}\simeq\mathfrak{sl}(2)$ be a subalgebra, and let $\mathfrak{t}$ be a Cartan subalgebra of $\mathfrak{k}$. F…