The Green scalar product formula for symmetric functions

Let $n$ be the fixed positive integer in the construction, let $\mathbf{K}\simeq \Gamma\otimes\mathbb{C}[v,v^{-1}]$, and let $\langle\;,\;\rangle_G$ denote Green's scalar product. For partitions $\lambda$ and $\mu$, write $p_\lambda$ and $p_\mu$ for the corresponding power-sum symmetric functions, $|\lambda|$ for the size of $\lambda$, $l(\lambda)$ for its length, and $z_\lambda$ for the standard symmetric-group factor. Green's scalar product conjecture. The restriction of Green's scalar product to $\mathbf{K}$ satisfies

$$(p_\lambda,p_\mu)=\delta_{\lambda\mu}z_{\lambda}q^{(n-1)|\lambda|}(1-q^{-1})^{n|\lambda|}\prod_{i=1}^{l(\lambda)}\frac{1-q^{n\lambda_i}}{(1-q^{\lambda_i})^2}.$$

This formula predicts the scalar product on the symmetric-function realization of the algebra $\mathbf{K}$ and extends the familiar Schur-function picture arising when $n=1$. The supplied text gives no evidence that the conjecture has been proved or disproved.