In this article, we give a class of representations of toroidal extended affine Lie algebras on Fock spaces based on a special subset of roots. Several properties of these roots are discussed. Then with these properties we find the singular vectors in the representations. After that we construct anti-linear anti-involutions of these Lie algebras and hermitian forms on the representations. At last, we find the sufficient and necessary conditions to guarantee that the representations are unitarizable.
2020 Mathematics Subject Classification. Primary: 17B67, 17B10; Secondary: 17B05, 17B22.