CHARACTERS AND REPRESENTATIONS OF NEW FERMIONIC W-ALGEBRAS

W-algebras are extensions of the Virasoro algebra describing chiral subalgebras of conformal quantum field theories. Careful analysis of the four-point functions and consideration of the invariant spaces under a subgroup of the modular group SL (2, Z) allow one to find all representations of new classes of fermionic W-algebras constructed recently. For each of these W-algebras there exists only a finite number of representations. The corresponding fusion rules are calculated.