Two-parameter generalization for the super modified KP hierarchy in super Fock spaces

This paper presents a construction of the ( λ, n )-generalized super modified KP (SmKP) hierarchy, an extended integrable system that contains the standard super modified KP hierarchy as the special case λ = 0 , where λ is a non-negative integer and n a positive integer. The construction relies on an explicit embedding of the affine superalgebra a ^ n | n into the infinite dimensional Lie superalgebra a ∞ | ∞ . Central to the work is the operator S ( λ,n ) , which commutes with the tensor product representation of the affine superalgebra a ^ n | n ( g ) and generates a hierarchy of bilinear equations. Specializing the parameters ( λ, n ) yields concrete super Hirota bilinear equations.