A symmetric bilinear form on a certain subspace Tb of a completion of the Fock space Tb is defined. The canonical and dual canonical bases of Tb 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 Tb expanded in terms of the standard monomial basis of Tb is obtained. Combining with the Brundan's algorithm for computing the elements in the canonical basis of Tb st, we have an algorithm computing the elements in the canonical basis of Tb for arbitrary b.
All Science Journal Classification (ASJC) codes