Large-spin models have recently gained significant attention due to experimental breakthroughs in cold atom systems. These setups enable highly controlled experiments that simulate complex theoretical models. However, large-spin models present considerable challenges for numerical modeling. The large spin dimensions and intricate symmetries of these systems make simulations extremely difficult, and standard methods often fall short, failing to access certain experimental regimes of interest. In this context, an alternative approach based on advanced group theory concepts was recently proposed by one of the project supervisors[1,2]. It avoids the traditional bottleneck of computing Clebsch-Gordan coefficients by directly implementing the SU(N) algebra in its most efficient mathematical basis: the basis of (semi-)standard Young tableaux (SYT). This breakthrough has already enabled simulations of systems at unprecedented scales with an exact implementation of all symmetries. This internship aims to explore and extend this new framework. The successful candidate will investigate one of the following research avenues, according to their interests and skills: 1) generalization to other symmetry groups. 2) Monte-Carlo/machine learning simulations of SU(N) models. [1] Wan et al, Phys. Rev. B 96, 115159 (2017) [2] Botzung et al, Phys. Rev. Lett. 132, 153001 (2024)