q-Virasoro algebra, q-conformal dimensions and free q-superstring

The commutators of standard Virasoro generators and fields generate various representations of the centreless Virasoro algebra depending on a conformal dimension J of the field in question (J is related to the Bargmann index of SU(1,1) generated by L(m), m = 0, +/- 1). We introduce the notion of q-conformal dimension for various oscillator realizations of q-deformed Virasoro (super)algebras proposed earlier, We use the field theoretical approach introduced recently in which the q-Virasoro currents L(alpha)(z) are expressed as Schwinger-like point-split normally ordered quadratic expressions in elementary fields, We extend this approach and probe the elementary fields A(z) (the q-superstring coordinate, momentum and fermionic field) and their powers by the q-Virasoro generators L(m)(alpha) (i.e. we calculate the commutators [L(m)(alpha), A(z)]) and show that to all of them can be assigned just the standard non-deformed conformal dimension.