9 problems

Let $G_{\mathbb{R}}$ be a real reductive group, and let an irreducible Harish-Chandra representation of $G_{\mathbb{R}}$ with real infinitesimal character be realized as the global…

Let $G$ be a real reductive group, let $\mathfrak{g}$ be its complexified Lie algebra, and let $\lambda\in\mathfrak{h}^*_{\mathbb{R}}$ be dominant. Let … be the Hodge global-sectio…

Let $\lambda \in \mathfrak{h}^*_{\mathbb{R}}$ be dominant, let $\mathcal{M}$ be a polarized Hodge module of weight $w$, and let $S$ be its polarization. Its globalization is the tu…

Let $X$ be a complex algebraic variety. Let $\C_X$ be $Perv(X,\mathbb{C})$ or $\mathbf{D}^b_c(X,\mathbb{C})$, and let $S=\{\mathcal{F}\}\subset\operatorname{Iso}(\C_X)$ consist of…

Let $G/P$ and $G/Q$ be the homogeneous spaces under consideration, with $Z_0,\ldots,Z_k$ the $G$-orbits in $G/P\times G/Q$, ordered by decreasing size. Let $j:Z_0\to G/P\times G/Q$…

Hodge-module open-orbit equivalence conjecture. The object $\mathcal{T}$ is the kernel of an equivalence

Let $\mathcal M^{\rm mix}$ be the graded subcategory from the Hodge-theoretic Koszul duality conjecture. Let $\kappa$ be the functor from $K$-equivariant coherent sheaves on…

Let $G_{\mathbb R}$ be a real group with Cartan decomposition $\mathfrak g=\mathfrak k\oplus\mathfrak p$, let $\mathcal M_{\rm Ho}$ be the full subcategory of $K$-equivariant Hodge…

Let ${\mathcal{MH}}_{U\check{\ }}({ G\check{\ }}/{B\check{\ }})$ be the category of mixed Hodge modules on ${ G\check{\ }}/{B\check{\ }}$ equivariant with respect to…