Representations of Generalized a$_r$ Statistics and Eigenstates of Jacobson Generators

We investigate a generalization of $A_r$ statistics discussed recently in the literature. The explicit complete set of state vectors for the $A_r$ statistics system is given. We consider a Bargmann or an analytic function description of the Fock space corresponding to $A_r$ statistics of bosonic kind. This brings, in a natural way, the so-called Gazeau-Klauder coherent states defined as eigenstates of the Jacobson annihilation operators. The minimization of Robertson uncertainty relation is also considered.