14 problems

Let $G$ be a connected semisimple Lie group with finite center, let ${\bf g}$ be its Lie algebra, and let $K$ be a maximal compact subgroup. Let $(\pi,V_{\pi,K})$ be a Harish-Chand…

Let $\mathfrak{p}$ be a very nice parabolic subalgebra with associated Levi subgroup $L_{0}$, stable Levi factor $\mathfrak{l}$, and nilradical $\mathfrak{n}$. Let $M$ be a Harish-…

Uniform finiteness conjecture. One has

Weight-dependence conjecture. There exists a constant $C=C_G>0$ depending only on $G$ such that

Cohen–Macaulay conjecture. The $\mathbb{C}[\OO_K]$-module

Vogan's conjecture. There is an isomorphism of $K$-representations

Generic-character simplicity conjecture. The module $Q(0,\chi)$ is simple.

Let $G_{\mathbb{R}}$ be a real reductive group with maximal compact subgroup $K$, complexified Lie algebra $\mathfrak{g}$, and associated decomposition…

Let $G$ be a reductive group with symmetric subgroup $K=G^\theta$, let $P$ be a $\theta$-minimal parabolic with unipotent radicals $N$ and $N^-$, and let $M_K=K\cap P$. Write…

Let $i$ be the inclusion of the relevant $K$-orbit, let $\phi$ be the corresponding local system, and let $i_!\phi$ and $i_+\phi$ denote its minimal and maximal extensions as…

Let $\widetilde K$ be the spin cover of a maximal compact subgroup $K$, and let $\mathsf{I}_{\mathrm{Dir}}(X)$ denote the Dirac index of a finite-length Harish-Chandra module $X$.…

Let $\mathcal{H}(\chi)_{\mathbb O}$ be the Harish-Chandra category associated with a nilpotent orbit $\mathbb O$, and let ${}^\chi \mathcal{H}^K_{\mathbb O}$ be the full subcategor…

Let $X$ be an irreducible Harish-Chandra $(\mathfrak{g},K)$-module, and let … be the irreducible decomposition of its associated variety. The graph…

Let $\mathfrak{k}\subset\mathfrak{g}$ be a reductive in $\mathfrak{g}$ subalgebra. A $(\mathfrak{g},\mathfrak{k})$-module is multiplicity free if every simple $\mathfrak{k}$-module…