(q,t)-hook formula for Birds and Banners

We study Okadas conjecture on $(q,t)$-hook formula of general $d$-complete posets. Proctor classified $d$-complete posets into 15 irreducible ones. We try to give a case-by-case proof of Okadas $(q,t)$-hook formula conjecture using the symmetric functions. Here we give a proof of the conjecture for birds and banners, in which we use Gaspers identity for VWP-series ${}_{12}W_{11}$.