  In this paper, following a similar procedure developed by Buttcane and Miller
in \cite{MillerButtcane} for $SL(3,\RR)$, the $(\frakg,K)$-module structure of
the minimal principal series of real reductive Lie groups $SU(2,1)$ is
described explicitly by realizing the representations in the space of
$K$-finite functions on $U(2)$. Moreover, by combining combinatorial techniques
and contour integrations, this paper introduces a method of calculating
intertwining operators on the principal series. Upon restriction to each
$K$-type, the matrix entries of intertwining operators are represented by
$\Gamma$-functions and Laurent series coefficients of hypergeometric series.
The calculation of the $(\frakg,K)$-module structure of principal series can be
generalized to real reductive Lie groups whose maximal compact subgroup is a
product of $SU(2)$'s and $U(1)$'s.
