An inversion formula for some Fock spaces

A symmetric bilinear form on a certain subspace T^b of a completion of the Fock space T^b is defined. The canonical and dual canonical bases of T^b are dual with respect to the bilinear form. As a consequence, the inversion formula connecting the coefficients of the canonical basis and that of the dual canonical basis of T^b expanded in terms of the standard monomial basis of T^b is obtained. Combining with the Brundan's algorithm for computing the elements in the canonical basis of T^b _st, we have an algorithm computing the elements in the canonical basis of T^b for arbitrary b.