arXiv2026
Let $Q$ be a bipartite Dynkin quiver of finite simply-laced type and $\mathscr C_Q$ the corresponding Hernandez--Leclerc category. We study a two-parameter specialization of the Fedele--Hernandez toroidal Grothendieck ring and identify its generic positive part with a Cartan-type multiparameter quantum group. The structural input is the identity \[ 2D^{(2)}-D_0=ω_Q\circ(°_Q,°_Q), \] where $D_0,D^{(2)}$ are the two effective toroidal commutation forms and $ω_Q$ is the antisymmetric Euler form of \(Q\). It realizes the specialized character algebra, after an auxiliary scalar extension, as a graded bicharacter twist of the one-parameter algebra at $v=t_0t^{1/2}$. This yields the required root grading and PBW graded dimensions. For every source--sink edge $r\to s$, these dimensions combine with the local \(A\)--\(Y\) commutation formula to give a quadratic annihilator for \(\operatorname{Ad}_{Z_r}\). Consequently \[ \operatorname{Spec}_{Z_r}(Z_s)=\{t_0t,t_0^{-1}\}, \] without thinness or type-specific character formulas. The two spectral values yield the oriented multiparameter Serre relations. With \[ q_{ii}=t_0^2t,\qquad q_{ij}=t_0^{-1},\qquad q_{ji}=t_0^{-1}t^{-1}\quad(i\to j), \] and \(q_{ij}=1\) on nonedges, we obtain \[ U_{\mathbf q}^{+}(\mathfrak g) \simeq \mathscr K_\infty(\mathscr C_Q)\otimes_RK \] for $\mathfrak g$ of type $A_n,D_n,E_6,E_7,E_8$.