On symmetries of the Duflo–Serganova functor

Abstract We initiate a study of the symmetries of the Duflo–Serganova functor, DS . In particular we give new constructions of Lie superalgebras, Lie supergroups, and associative superalgebras which act on this functor. The main result is a realization that in the Kac–Moody setting, we find new odd infinitesimal symmetries of DS . In addition, we connect our work to a computation of Heidersdorf and Weissauer which computed DS x for a maximal rank x on Kac-modules for GL( n ∣ n ), and extend the ideas and results to P ( n ).