Deforming maps for Lie group covariant creation and annihilation operators

Any deformation of a Weyl or Clifford algebra 𝒜 can be realized through a “deforming map,” i.e., a formal change of generators in 𝒜. This is true in particular if 𝒜 is covariant under a Lie algebra g and its deformation is induced by some triangular deformation $Uhg$ of the Hopf algebra $Ug.$ We propose a systematic method to construct all the corresponding deforming maps, together with the corresponding realizations of the action of $Uhg.$ The method is then generalized and explicitly applied to the case that $Uhg$ is the quantum group $Uhsl(2).$ A preliminary study of the status of deforming maps at the representation level shows in particular that “deformed” Fock representations induced by a compact $Uhg$ can be interpreted as standard “undeformed” Fock representations describing particles with ordinary Bose or Fermi statistics.