Fock space representations of Bogolyubov transformations as spin representations

The representation on a Fock space of the group Bogolyubov transformations is recognized as spin an orthogonal group. Derivations based this observation some known formulas for overlap amplitude two quasifermion vacuum states that are in cases more complete than those literature shown. It pointed out name ``Onishi formula'' assigned to different expressions which related but have scopes. One them has what been described sign problem; other one, due Onishi and Yoshida, limited scope no problem. I give short proof latter, whose derivation missing paper by new, combinatoric, equivalent formula recently derived Robledo.