We present an overview of the method of Neural Quantum States applied to the many-body problem
of atomic nuclei. Through the lens of group representation theory, we focus on the problem of
constructing neural-network ansätze that respect physical symmetries. We explicitly prove that
determinants, which are among the most common methods to build antisymmetric neural-network
wave functions, can be understood as the result of a group convolution. We also identify the
reason why this construction is so efficient in practice compared to other group convolutional
operations. We conclude that group representation theory is a promising avenue to incorporate
explicitly symmetries in Neural Quantum States.