  We generalize the notion of Haldane pseudopotentials to anisotropic
fractional quantum Hall (FQH) systems which are physically realized, e.g., in
tilted magnetic field experiments or anisotropic band structures. This
formalism allows us to expand any translation-invariant interaction over a
complete basis, and directly reveals the intrinsic metric of incompressible FQH
fluids. We show that purely anisotropic pseudopotentials give rise to new types
of bound states for small particle clusters in the infinite plane, and can be
used as a diagnostic of FQH nematic order. We also demonstrate that generalized
pseudopotentials quantify the anisotropic contribution to the effective
interaction potential, which can be particularly large in models of fractional
Chern insulators.
