We show that Lusztig's canonical basis for the degree two part of the Grassmannian coordinate ring is given by \({\rm SL}_k\) web diagrams. Equivalently, we show that every \({\rm SL}_2\) web immanant of a plabic graph for \({\rm Gr}(k,n)\) is an \({\rm SL}_k\) web invariant.

Mathematics Subject Classifications: 05E10, 14M15, 20C30

Keywords: Grassmannians, webs, canonical basis, Catalan