5 problems

Let $M'$ and $M$ be Coxeter data belonging to classical series, and let $\operatorname{Hom}_{\mathscr H}(M',M)$ denote the homomorphisms of the corresponding Hecke monoids. A homom…

Let $(W(M),\star)$ and $(W(M'),\star)$ be Hecke monoids of irreducible crystallographic types. A homomorphism is injective parabolic if it is both injective and parabolic, and it i…

Let $M$ be a Coxeter matrix over $I$, let $W(M)$ be its Coxeter group with Hecke product $\star$, and let $\tilde{\mathsf P}(M)$ be the set of multiparabolic elements in $W(M)$. Su…

Let $M$ be a Coxeter matrix over $I$, let $\mathscr F(M)$ denote the relevant finite subsets, and let $p_J$ be the parabolic projection for $J\subset I$. For multiparabolic element…

Let $M(\mathbf d)$ be a Coxeter monoid and let $\mathbf T_{\mathbf d}$ be a Tits homomorphism associated with it. Injectivity conjecture. All Tits homomorphisms…