Representations of spin quiver Hecke algebras for orthosymplectic Lie superalgebras

TL;DR

This paper classifies all irreducible representations of spin quiver Hecke algebras associated with orthosymplectic Lie superalgebras, using dominant Lyndon words to explicitly construct cuspidal modules and standard representations.

Contribution

It provides a complete construction and classification of irreducible modules for these algebras, linking highest weights to dominant words and Lyndon words.

Findings

Irreducible representations correspond to dominant words.

Cuspidal modules are constructed via dominant Lyndon words.

Irreducible modules are simple heads of induced standard modules.

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.