# Secondary fan and KN strata

Let $$\mathbb{G}_m^r$$ act on the affine space $$\mathbb{A}^n$$ through an embedding into the open dense torus. Is there a way to calculate the 1-parameter subgroups that determine the KN strata from the structure of the secondary fan?

Suppose our chosen linearization/character $$\chi$$ lies in a maximal cone $$\sigma$$ in the secondary fan. I would like to say these 1PS's are the primitive cocharacters that pair to zero with the walls and pair negatively with the characters in $$\sigma$$, however I am having trouble understanding it.

Hope the question makes sense to the MO community.

I have an answer to this question now. The 1PS's for the KN strata have to depend on $$\chi$$ which determines the ordering, but one can also make noncanonical choices of 1PS's as in the question to simply describe the unstable loci as a union.