Well, Pauli principle sure plays a big role when we talk about the fermionic fields that coumpounds the Standard Model. Since the principle is expressed mathematicaly making the wave functions anti-symetric, you'll see this behavior in all the fermionic particles

GOOD....."Since the principle is expressed mathematical making the wave functions anti-symmetric"

Can you please elaborate/illustrate it?

Standard Model is mainly concerned with the unification of electroweak and strong forces and it us mathematically sound. In the development of its mathematical structure Pauli's exclusion principle does not play any explicit specific role except the anti-symmetric behaviour of fermion wave function, which follows from Fermi- Dirac statics also.

Siva Prasad Kodukula ,

the symmetry of the wave functions depends on what kind of particles you're describing. Suppose you have a system of bosonic particles, all identical (e.g., a system composed of mesons). If you change the places of two particles (like changing two eggs in a box), the wave function of the system remains the same - so it's a symmetric wave function. If, instead, you have a fermionic particles system (like electrons), exchanging two particles of places will change the sign of its wave function - so it's a anti-symmetric wave function. This fact leads to Pauli exclusion principle (see Spin–statistics theorem for detailed information).

Thus, all the particles that compounds the Standard Model described with anti-symmetric functions follows the Pauli principle.

It is well established fact that the particles with anti- symmetric wave function or the anti-commutation rule folliwed by thrir creation and anihilatiin operators

Sorry for discontinuity. The annihilation and creation operators of particle with antisymmetric wave function follow anti-commutation and hence Pauli's exclusion principle. But this principle does play any other specific role in the development of mathematical structure of Standard Model.