  In this paper we research all possible finite-dimensional representations and
corresponding values of the Barbero-Immirzi parameter contained in EPRL
simplicity constraints by using Naimark's fundamental theorem of the Lorentz
group representation theory. It turns out that for each non-zero pure imaginary
with rational modulus value of the Barbero-Immirzi parameter $\gamma = i
\frac{p}{q}, p, q \in Z, p, q \ne 0$, there is a solution of the simplicity
constraints, such that the corresponding Lorentz representation is finite
dimensional. The converse is also true - for each finite-dimensional Lorentz
representation solution of the simplicity constraints $(n, \rho)$, the
associated Barbero-Immirzi parameter is non-zero pure imaginary with rational
modulus, $\gamma = i \frac{p}{q}, p, q \in Z, p, q \ne 0$. We solve the
simplicity constraints with respect to the Barbero-Immirzi parameter and then
use Naimark's fundamental theorem of the Lorentz group representations to find
all finite-dimensional representations contained in the solutions.
