  We show that when $d \geq 3$, the Hilbert scheme
$Hilb_{dT+1-\binom{d-1}{2}}(G(k,n))$ has 2 components, even though elements in
both components have the same cohomology class. Moreover, we show that the
Hilbert scheme associated to the Hilbert polynomial
$\binom{T+n}{n}-\binom{T+n-d}{n}$ in Grassmannian has at most 2 connected
components.
