Quivers with relations arising from Koszul algebras of g-invariants

Let g be a complex simple Lie algebra and let Ψ be an extremal set of positive roots. After Chari and Greenstein (2009) [9], one associates with Ψ an infinite dimensional Koszul algebra which is a graded subalgebra of the locally finite part of (op(EndV)⊗Sg(g)), where V is the direct sum of all simple finite dimensional g-modules. We describe the structure of the algebra explicitly in terms of an infinite quiver with relations for g of types A and C. We also describe several infinite families of quivers and finite dimensional associative algebras arising from this construction.