  S. Orlik and M. Strauch have studied locally analytic principal series
representation for general $p$-adic reductive groups generalizing an earlier
work of P. Schneider for $GL(2)$ and related the condition of irreducibility of
such locally analytic representation with that of a suitable Verma module. In
this article, we take the case of $GL(n)$ and study the globally analytic
principal series representation under the action of the pro-$p$ Iwahori
subgroup of $GL(n,\mathbb{Z}_p)$, following the notion of globally analytic
representations introduced by M. Emerton. Furthermore, we relate the condition
of irreducibility of our globally analytic principal series to that of a Verma
module. Finally, using Steinberg tensor product theorem, we construct Langlands
base change of our globally analytic principal series to a finite unramified
extension of $\mathbb{Q}_p$, generalizing an earlier work of Clozel for
$GL(2)$.
