Unobstructed Stanley-Reisner Degenerations for Dual Quotient Bundles on \(G(2,n)\)

Let \(Q^*\) denote the dual of the quotient bundle on the Grassmannian \(G(2,n)\). We prove that the ideal of \(Q^*\) in its natural embedding has initial ideal equal to the Stanley-Reisner ideal of a certain unobstructed simplicial complex. Furthermore, we show that the coordinate ring of \(Q^*\) has no infinitesimal deformations for \(n>5\).