Subregular J-rings of Coxeter systems via quiver path algebras

We use quivers and their representations to bring new perspectives on the subregular J-ring JC of a Coxeter system (W,S), subring Lusztig's J-ring. prove that is isomorphic suitable quotient path algebra double quiver (W,S). Up Morita equivalence, such quotients include group algebras all free products finite cyclic groups. then study category mod-AK dimensional right modules AK=K⊗ZJC over an algebraically closed field K characteristic zero. Our results classifications systems for which semisimple, has finitely many simple up isomorphism, or bound dimensions modules.