6 problems

Let $R$ be the polynomial ring in the variables ${\bf x}$, and let $D_1,\ldots,D_d$ be the inversion factors associated to the basic representatives of a general linear…

Let $A$ be a finite-dimensional symmetric algebra. The algebra $A$ is $\tau$-tilting finite if it has only finitely many isomorphism classes of support $\tau$-tilting modules, and…

Symmetrising-form conjecture. The form $t_{W,\mathbf u}$ takes values in $A$ and is a symmetrising form on $\mathcal H(W,\mathbf u)$. This is the Hecke-algebra conjecture attribute…

Wolffhardt's conjecture. If $\operatorname{Sym}_R(M)$ is a $\operatorname{UFD}$, then

Let $\mathfrak{g}$ be a complex semisimple Lie algebra with fixed Borel subalgebra $\mathfrak{b}$, Cartan subalgebra $\mathfrak{h}\subset\mathfrak{b}$, and parabolic subalgebra…

Let $W$ be an irreducible complex reflection group, let $A$ be the coefficient ring, and write ${\mathcal{H}}(W,{\mathbf u})$ for its cyclotomic Hecke algebra. Let $B(W)$ be the br…