An inversion formula for some Fock spaces

A symmetric bilinear form on a certain subspace Tˆb of a completion of the Fock space TbTb is defined. The canonical and dual canonical bases of Tˆb 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 Tˆb expanded in terms of the standard monomial basis of TbTb is obtained. Combining with the Brundan's algorithm for computing the elements in the canonical basis of Tˆbst, we have an algorithm computing the elements in the canonical basis of Tˆb for arbitrary b.