Braided symmetric algebras and a first fundamental theorem of invariant theory for ${\mathrm{U}}_q(G_2)$

Hongmei Hu, Ruibin Zhang

We develop invariant theory for the quantum group ${\mathrm{U}}_q$ of $G_2$ at generic $q$ in the setting of braided symmetric algebras. Let ${\mathcal{A}}_m$ be the braided symmetric al…