Using the light ladder basis for Kuperberg's C2 webs, we derive triple clasp formulas for idempotents projecting to the top summand in each tensor product of fundamental representations. We then find explicit formulas for the coefficients occurring in the clasps, by computing these coefficients as local intersection forms. Our formulas provide further evidence for Elias's clasp conjecture, which was given for type A webs, and suggests how to generalize the conjecture to non-simply laced types.

Using Kuperberg's B2/C2 webs, 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 so5 ∼ = sp 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 = 0, the Karoubi envelope of the C2 web category is equivalent to the category of tilting modules for the divided powers quantum group U Z q (sp 4 ).

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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 sp 4 (and the associated quantum group). Our argument has very little dependence on the base field. As a result, we prove that when OE2 q ¤ 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 A q .sp 4 /.

We give a direct proof of a result of Sundaram and Stanley: that the dimension of the space of invariant vectors in a 2k-fold tensor product of the vector representation of sp 2n equals the number of (n + 1)-avoiding matchings of 2k points. This can be viewed as an extension of Schensted's theorem on longest decreasing subsequences. Our main tool is an extension of Viennot's geometric construction to the setting of up-down tableaux.