  A relation is established in the present paper between Dicke states in a
d-dimensional space and vectors in the representation space of a generalized
Weyl-Heisenberg algebra of finite dimension d. This provides a natural way to
deal with the separable and entangled states of a system of N = d-1 symmetric
qubit states. Using the decomposition property of Dicke states, it is shown
that the separable states coincide with the Perelomov coherent states
associated with the generalized Weyl-Heisenberg algebra considered in this
paper. In the so-called Majorana scheme, the qudit (d-level) states are
represented by N points on the Bloch sphere; roughly speaking, it can be said
that a qudit (in a d-dimensional space) is describable by a N-qubit vector (in
a N-dimensional space). In such a scheme, the permanent of the matrix
describing the overlap between the N qubits makes it possible to measure the
entanglement between the N qubits forming the qudit. This is confirmed by a
Fubini-Study metric analysis. A new parameter, proportional to the permanent
and called perma-concurrence, is introduced for characterizing the entanglement
of a symmetric qudit arising from N qubits. For d=3 (i.e., N = 2), this
parameter constitutes an alternative to the concurrence for two qubits. Other
examples are given for d=4 and 5. A connection between Majorana stars and zeros
of a Bargmmann function for qudits closes this article.
