14 problems

Let $B=\operatorname{End}_\Lambda(T_M)$, let ${\mathcal T}_B^{\rm cl}$ denote the relevant class of classical tilting $B$-modules, and let ${\mathcal F}(\Delta)$ be the category de…

Let $(W,P)$ be a parabolic Coxeter system with generators $s_i\in S_W$, and let $\mathcal{H}_{(W,P)}$ be the category algebra of the Elias–Libedinsky–Williamson anti-spherical Heck…

Let $r$ be a nonnegative integer, let $\Bbbk$ be the underlying field, and let $S_\Bbbk(r,r)$ be the classical Schur algebra. An $i$-faithful quasi-hereditary cover means a quasi-h…

The q-ordering gap conjecture. For every non-hereditary algebra $A$,

Let $A$ be an algebra with iso-class of simple modules $\mathcal{S}$, where $|\mathcal{S}|=n$. A total ordering on $\mathcal{S}$ is a $q$-ordering if every Weyl module is Schurian…

Conjugacy conjecture. There exists an invertible element $x\in R$ such that

Let $n$ and $r$ be positive integers, let $q$ be the parameter, let $Q$ be the second parameter, and let $\mathcal{L}^n(2r-1)$ denote the algebra under consideration. Quasi-heredit…

Let $A_R$ be a based quasi-hereditary algebra over $R$ with conforming heredity data, and let $A'_R$ be a Ringel dual of $A_R$. Let $T^A(n,d)_\mathbb{F}$ and…

Let $A$ be a based quasi-hereditary algebra, let $A'$ be a Ringel dual of $A$, and let $d\leq n$. For a suitable degree-zero subalgebra $\mathfrak{a}$ of $A$, consider the generali…

Let $(P,\leq)$ be a finite poset. Denote by $Z_n$ the partially ordered set whose Hasse diagram is a zig-zag orientation of an affine quiver of type $\mathbb{A}_n$. Lattice conject…

Let $S_{Q,q}^\mathrm{B}(n,d)$ be the type B $q$-Schur algebra, and let $f^\mathrm{B}_d(Q,q)$ denote the parameter whose invertibility is the condition in the preceding quasi-heredi…

Let $T^{\bar{Z}}_{\bar{\mathfrak z}}(n,d)$ be the generalized Schur algebra, Morita equivalent to weight $d$ RoCK blocks of symmetric groups and the corresponding Hecke algebras. T…

Bobiński–Malicki conjecture.

Par's non-formality conjecture. The extension algebra $\Gamma$ in the $n=2$ case is not formal.