15 problems

Let $\Catgeomdk$ be the geometric category defined in the surrounding text, let $\Pervsmkb$ be the stated target category, and let $\ConvHecke$ be the functor constructed there. Co…

Let $\Catgeom$ be the abelian category of objects equipped with compatible Hecke isomorphisms, and call an object finitely generated if it admits a surjection from an object of the…

Hecke-category action conjecture. Assigning $B_s$ to $\theta_s$ for every simple reflection $s$ induces a right action of the Hecke category $\mathcal{D}$ on…

The w₀-dual and diagonal cell conjecture. $w_0$-dual cells, respectively diagonal cells, should have isomorphic asymptotic Hecke categories.

Let $(W,S)$ be a Coxeter system of type $\operatorname{\textbf{B}}_n$, let $\operatorname{\mathfrak{h}}$ be a Cartan realisation of the same type, and let $I\subset S$ be a parabol…

Let $W$ be the Weyl group of type $\operatorname{\textbf{C}}_n$, with $I\subseteq S$ of type $\operatorname{\textbf{A}}_{n-1}$, and identify elements of the relevant parabolic quot…

Let $(W,P)$ and $(W',P')$ be parabolic Coxeter systems, and let $\boldsymbol{\beta}$ denote an isomorphism between closed subsets $\Sigma\subseteq W$ and $\Sigma'\subseteq W'$ that…

Categorical p-half-twist conjecture. For any $w$ in the $p$-cell $\lambda$,

Categorical half-twist conjecture. If $w$ lies in the cell $\lambda$, then

Let $G$ be the reductive group underlying the spherical Hecke category, and let … be the bubbling spherical Hecke category, equipped with its monoidal structure. The E3-structure c…

Let $(W,S)$ be a two-colored realization over a field $\Bbbk$, with colors $s$ and $t$, and let $JW_{n_s}$ and $JW_{n_t}$ denote the corresponding Jones-Wenzl projectors. Write…

Let $G$ be a connected reductive algebraic group over an algebraically closed field $\Bbbk$ of characteristic $p$ strictly bigger than the Coxeter number of $G$. Let…

Let $X$ be a Bott–Samelson bimodule, let $W$ be the relevant Weyl group, and write … where the $B_w$ are indecomposable objects. Let $F_1$ be the maximal finite-dimensional…

Let $\widetilde\kappa$ be the derived equivalence between the mixed derived category on the flag variety and the corresponding category on the dual group’s quotient, satisfying the…

For a reductive algebraic group in positive characteristic, consider the principal block of its category of representations and the translation functors between its blocks. Hecke-c…