Web calculus and tilting modules in type \(C_2\) (Q2697603)

Summary: Using Kuperberg's web calculus (1996), and following Elias and Libedinsky, we describe a ``light leaves'' algorithm to construct a basis of morphisms between arbitrary tensor products of fundamental representations for \(\mathfrak{s} \mathfrak{p}_4\) (and the associated quantum group). Our argument has very little dependence on the base field. As a result, we prove that when \([2]_q \neq 0\), the Karoubi envelope of the \(C_2\) web category is equivalent to the category of tilting modules for the divided powers quantum group \(U_q^{\mathcal{A}} (\mathfrak{sp}_4)\).