A flag matroid of whose constituent matroids have ranks $r_1, \ldots, r_k$ and ground set size $n$ defines a KClass on the (partial) flag variety $Fl(r_1,\ldots, r_k;n)$. When the flag matroid arises from a matrix representing a point on the (partial) flag variety, this equivariant K-class coincides with that of the structure sheaf of its torus orbit closure. See [CDMS18] or [DES20].
i1 : X = generalizedFlagVariety("A",2,{1,2}) o1 = a GKM variety with an action of a 3-dimensional torus o1 : GKMVariety |
i2 : A = matrix{{1,2,3},{0,2,3}} o2 = | 1 2 3 | | 0 2 3 | 2 3 o2 : Matrix ZZ <--- ZZ |
i3 : FM = flagMatroid(A,{1,2}) o3 = a flag matroid with rank sequence {1, 2} on 3 elements o3 : FlagMatroid |
i4 : C1 = makeKClass(X,FM) o4 = an equivariant K-class on a GKM variety o4 : KClass |
i5 : C2 = orbitClosure(X,A) o5 = an equivariant K-class on a GKM variety o5 : KClass |
i6 : C1 === C2 o6 = true |