locally analytic representations of $p$-adic analytic groups have played a crucial role in many areas of arithmetic and representation theory (including in $p$-adic local langlands program) since their introduction by schneider and teitelbaum. in this talk we will briefly review some aspects of the theory of locally analytic representations. then, for a locally analytic representation $v$ of $gl_2(f)$ we will construct a coefficient system attached to the bruhat-tits tree of $gl_2(f)$. finally we will use this coefficient system to construct a resolution for locally analytic principal series of $gl_2(f)$.