On the behavior of the periodic Coxeter Laplacian in some representations related to the antiferromagnetic asymptotic mode and continual limits

We consider some problems related to the asymptotic behavior of the so-called periodic Coxeter Laplacian (a distinguished operator in the group algebra of the symmetric group essentially coinciding with the Hamiltonian of the XXX Heisenberg model of spins) in some representations corresponding to the antiferromagnetic asymptotic mode, as well as in some related continual limits.