A condition on a matroid of rank $n-2$ for the corresponding thin Schubert cell being nonempty is determined. A necessary and sufficient condition for $k$ and $n$ so that the closure of a thin Schubert cell in $G(k,n)$ is always a union of thin Schubert cells is given.
J. Math. Kyoto Univ.
48(2):
265-275
(2008).
DOI: 10.1215/kjm/1250271412
