COSET CONSTRUCTION AND CHARACTER SUM-RULES FOR THE DOUBLY EXTENDED N=4 SUPERCONFORMAL ALGEBRAS

Character sum rules associated with the realization of the N = 4 super conformal algebra A(gamma) on manifolds corresponding to the group cos ets SU(3)k+/U(1) are derived and developed as an important tool in obt aining the modular properties of A(gamma) characters as well as inform ation on certain extensions of that algebra. Their structure strongly suggests the existence of rational conformal field theories with centr al charges in the range 1 less-than-or-equal-to c less-than-or-equal-t o 4. The corresponding characters appear in the massive sector of the sum rules and are completely specified in terms of the characters for the parafermionic theory SU(3)/(SU(2)xU(1)) and in terms of the branch ing functions of massless A(gamma) characters into SU(2)k+xSU(2), char acters.