3 problems

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Berenstein–Kazhdan's presentation conjecture for the algebra ${\bf D}(W)$
Berenstein–Kazhdan's presentation conjecture. The algebra ${\bf D}(W)$ is generated by the $D_s$ subject to the idempotent relations $D_s^2=D_s$ , the braid relations
Conjecturesolvedalgebra-presentations coxeter-groups hecke-hopf-algebrasarXiv posted 2 days ago
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Berenstein–Kazhdan's module-algebra conjecture for crystallographic Coxeter groups
Berenstein–Kazhdan's conjecture. These assignments turn ${\mathcal L}_I$ into an ${\bf H}(W)$ -module algebra.
Conjecturesolvedcoxeter-groups hecke-hopf-algebras module-algebrasarXiv posted 2 days ago
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The generalized Cartan matrix module-algebra conjecture for Hecke-Hopf algebras
Let $A=(a_{ij})$ , $i,j\in I$ , be a generalized Cartan matrix, and let $W=W_A$ be the corresponding crystallographic Coxeter group, with … for $i\ne j$ . Let…
Conjectureopencoxeter-groups generalized-cartan-matrices hecke-hopf-algebrasarXiv posted 2 days ago

Berenstein–Kazhdan's presentation conjecture for the algebra D(W){\bf D}(W)D(W)