Representations of spin quiver Hecke algebras for orthosymplectic Lie superalgebras

Abstract

We construct all the irreducible representations of spin quiver Hecke algebras for orthosymplectic Lie superalgebras osp(1|2n), and show that their highest weights are given by the dominant words. We use the dominant Lyndon words to construct the cuspidal modules and show that the irreducible representations are the simple heads of standard representations constructed by induction from the cuspidal modules.