Triple clasp formulas for $C_2$ webs

TL;DR

This paper derives explicit formulas for clasp idempotents in $C_2$ webs using the light ladder basis, providing evidence for Elias's clasp conjecture and suggesting generalizations to non-simply laced types.

Contribution

It introduces triple clasp formulas for $C_2$ webs and computes coefficients as local intersection forms, advancing understanding of clasp structures in non-$A$ types.

Findings

Explicit formulas for clasp coefficients in $C_2$ webs.

Evidence supporting Elias's clasp conjecture.

Potential pathways for generalizing clasp conjectures.

Abstract

Using the light ladder basis for Kuperberg's $C_2$ 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.