The generalised Saxl conjecture for finite Coxeter groups

Let $W$ be any finite Coxeter group. Let $\operatorname{Irr}(W)$ be its irreducible characters, and call a family $F$ of $\operatorname{Irr}(W)$ good if it contains a character occurring as a $W$-constituent of $\widetilde{\sigma}\otimes\mathcal{S}$ for some genuine irreducible representation $\widetilde{\sigma}$ in the minimal-eigenvalue set of the Pin-cover central element. The generalised Saxl conjecture for Coxeter groups. The representation

$$\left(\bigoplus_{\sigma\in F:\ F\text{ is good}}\sigma\right)^{\otimes 2}$$

contains every irreducible character of $W$.

This extends the Weyl-group formulation to arbitrary finite Coxeter groups and is motivated by the spinorial description of good Lusztig families; the source notes that the non-crystallographic cases are included in this broader setting.