Title: On the presentation of Hecke-Hopf algebras for non-simply-laced type,
Abstract: Hecke-Hopf algebras were defined by A. Berenstein and D. Kazhdan. We give an
explicit presentation of an Hecke-Hopf algebra when the parameter $m_{ij},$
associated to any two distinct vertices $i$ and $j$ in the presentation of a
Coxeter group, equals $4,$ $5$ or $6$. As an application, we give a proof of a
conjecture of Berenstein and Kazhdan when the Coxeter group is crystallographic
and non-simply-laced. As another application, we show that another conjecture
of Berenstein and Kazhdan holds when $m_{ij},$ associated to any two distinct
vertices $i$ and $j,$ equals $4$ and that the conjecture does not hold when
some $m_{ij}$ equals $6$ by giving a counterexample to it.