Closure relations for totally nonnegative cells in $G/P$.

The totally nonnegative part of a partial flag variety G/P has been shown in We show that the closure of a cell is a union of cells and give a combinatorial description of the closure relations. The totally nonnegative cells are defined by intersecting (G/P ) 0 with a certain stratification of G/P defined by Lusztig We also verify the same closure relations for these strata.