I am reading notes of Samuel Marks on ”Galois Representations”. In this paper, on page 14 (definition 3.1), it is said that given a representation $\rho$ of $Gal(L/K)$ it yields another representation $\rho^{I_p}$ but this time not on $V$ but on $V^{I_\mathfrak{\beta}}$. How exactly is this representation $\rho^{I_p}$ defined? Also, as there is no reference to $p$ before, I am believing that those $p$’s on this page must be $\mathfrak{p}$ instead, am i right?
Thank you in advance…