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
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i2 : A = matrix{{1,2,3},{0,2,3}}
o2 = | 1 2 3 |
| 0 2 3 |
2 3
o2 : Matrix ZZ <-- ZZ
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i3 : FM = flagMatroid(A,{1,2})
o3 = a "flag matroid" with rank sequence {1, 2} on 3 elements
o3 : FlagMatroid
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i4 : C1 = makeKClass(X,FM)
o4 = an "equivariant K-class" on a GKM variety
o4 : KClass
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i5 : C2 = orbitClosure(X,A)
o5 = an "equivariant K-class" on a GKM variety
o5 : KClass
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i6 : C1 === C2
o6 = true
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