I am reading through Representations of $\mathfrak p$-adic groups (P. Cartier, Corvallis proceedings Vol I) and had a question about the following section. $G$ is a topological group of totally disconnected type.
I'm confused on the definition of the space $V_{\mathfrak d}$. Isn't a "minimal $K$-invariant subspace of $V$ affording a representation of $K$ of class $\mathfrak d$" nothing more than an isomorphic copy of $\mathfrak d$ occuring as a $K$-invariant subspace of $V$?