I want to know what mathematical theories I should be aware of for a deep understanding of the standard particles model.
This depends on what you already know, but if you know some quantum field theory, then getting to know the $SU(N)$ groups is a good start.
This is because the standard model is built upon Gauge-symmetry under these groups. The symmetry group of the standard model is:
$$SU(3) \times SU(2) \times U(1)$$
The $SU(3)$ is the symmetry of the strong force under the echange of colour. The $SU(2) \times U(1)$ is the symmetry group of the electroweak sector.