Abstract
<jats:p>We investigate relations between the group of symmetries of a subspace of the symmetric tensor product of a separable Hilbert space and a representation of the partition function of a quantum entangled family of particles associated with this subspace. Consider a system of $N$ noninteracting identical bosons. In general, the system is described by the $N$-fold symmetric tensor product $\mathcal{E}^{\odot N},$ where $\mathcal{E}$ is the Hilbert space that describes the one-particle system. In some cases, the system can be described by some subspace of $\mathcal{E}^{\odot N}.$ We consider the case in which this subspace is the closure of the linear span of some subset of the eigenbasis of the Hamiltonian of the system. We describe the group of symmetries $S$ such that the partition function of the system is $S$-symmetric.</jats:p>