Gauge origami and quiver W-algebras. Part III. Donaldson-Thomas qq-characters

A bstract We further develop the BPS/CFT correspondence between quiver W-algebras/ qq -characters and partition functions of gauge origami. We introduce qq -characters associated with multi-dimensional partitions with nontrivial boundary conditions which we call Donaldson-Thomas (DT) qq -characters. They are operator versions of the equivariant DT vertices of toric Calabi-Yau three and four-folds. Moreover, we revisit the construction of the D8 qq -characters with no boundary conditions and give a quantum algebraic derivation of the sign rules of the magnificent four partition function. We also show that under the proper sign rules, the D6 and D8 qq -characters with no boundary conditions all commute with each other and discuss its physical interpretation.