  In the large rank limit, for any nonexceptional affine algebra, the graded
branching multiplicities known as one-dimensional sums, are conjectured to have
a simple relationship with those of type A, which are known as generalized
Kostka polynomials. This is called the X=M=K conjecture. It is proved for
tensor products of the symmetric power Kirillov-Reshetikhin modules for all
nonexceptional affine algebras except those whose Dynkin diagrams are
isomorphic to that of untwisted affine type D near the zero node. Combined with
results of Lecouvey, this realizes the above one-dimensional sums of affine
type C, as affine Kazhdan-Lusztig polynomials (and conjecturally for type D).
