The super BKP hierarchy from Clifford super module

Abstract

The super BKP (SBKP) hierarchy in fermionic picture is constructed by embedding tensor product of infinite-dimensional Lie superalgebra of type B and Grassmann algebra into Clifford superalgebra. On the basis of bosonic counterpart, we construct the super Baker functions of the SBKP hierarchy and give a bilinear identity represented by it. The super differential operator is introduced and the bilinear identity in terms of the super pseudo-differential operator is shown. Finally, the solutions of non group orbits in the super fermionic Fock space are discussed.