Let $F$ be a local field of characteristic 0.


I am wondering whether an unramified principal series representation of $\operatorname{GL}\_n(F)$ can have 1-dimensional quotient when $n>1$.


In some paper, the author claims that it can’t.


Do you know the reason?



Subquotient of principal series
Think of $Ind\_B^G 1$ as smooth functions on $G/B$ and look at the subspace of constant functions. 


