Let $\rho$ be a Weil representation over a local field $K$. In this paper, I found the following defintion of the local polynomial:
$$ P(\rho,T) = \det(1-\operatorname{Frob}_K^{-1}T | \rho^{I_K}). $$
Could you please explain me what this notation means? I am especially confused by the $\rho^{I_K}$ at the end. I just know that $I_K$ is the inertia subgroup of the absolute Galois group $G_K$. And I assume that $T$ is just the variable of the polynomial, right?
Thank you in advance!