Polynomial generation conjecture for the K-homology of the symplectic loop group

Let $Sp(n)$ be the compact symplectic group, let $U(i)$ be the unitary group, and let $K.\Omega Sp(n)$ denote the K-homology ring of its based loop space. For $1\leq i\leq n$, the subvariety $Sp(i)/U(i)\subset Sp(n)/U(n)$ determines a $K$-homology fundamental class $[Sp(i)/U(i)]$, whose reduction is $[Sp(i)/U(i)]-1$. Polynomial generation conjecture. The $K$-homology ring $K.\Omega Sp(n)$ is polynomial on the classes represented by the reduced $K$-homology fundamental classes

$$[Sp(i)/U(i)]-1,$$

for $1\leq i\leq n$. The claim would give a representation-theoretic description of the generators of the twisted-related K-homology computation, replacing the homological generators in dimensions $4i-2$ by classes arising from the natural subvarieties $Sp(i)/U(i)$. The source presents this as an apparent generation phenomenon and provides no resolution, so its status remains open.