The infinite series representation of the generalized Bose operator given by Brandt and Greenberg is shown to be equal to an operator introduced by Demkov.
We define a new set of squeezed states using group-theoretical methods. The definition is based on the Holstein-Primakoff realization of both SU(2) and SU(1,1). Generalizations of these realizations are presented, connected with the Brandt-Greenberg generalized Bose operators. The new states exhibit interesting squeezing properties, depending in a characteristic way on the dimension of the irreducible unitary representation adopted. We also discuss the asymptotic behavior and present a set of relevant numerical results. Unexpected and interesting scaling behavior appears.