The type C K-Stanley expansion conjecture in GQ functions

Let $w$ be a signed permutation. For each strict partition $\lambda$, let $GQ_\lambda$ denote the corresponding GQ symmetric function, let $a^C_w(\lambda)$ be the coefficient determined by the stated SDT insertion method, let $\ell(w)$ be the length of $w$, and let $\beta$ be the $K$-theoretic parameter.

Type C K-Stanley expansion conjecture.

$$G^C_w = \sum_{\lambda\ \mathrm{strict}} \beta^{|\lambda| - \ell(w)}a^C_w(\lambda) \cdot GQ_\lambda.$$

This conjecture proposes an expansion of every Type $C$ $K$-Stanley function in the basis of GQ functions, with coefficients arising from the insertion objects described in the paper. It extends the relation between GQ functions and Type $C$ $K$-Stanley functions established for the specified elements associated with strict partitions and positive integers.