Polynomials having leading terms over C2 in the Fock space

We characterize polynomials p having leading terms over C2 in a generalized sense. As applications, we study a quasi-invariant subspace [p] generated by p in the Fock space, and show that a quasi-invariant subspace M is similar to [p] if and only if M=[q] for some polynomial q having the same leading term as p. These are generalizations of Guo and Hou's work.