Abstract: |
We introduce a new concept of "shift system", which is a purely Lie algebraic formulation of the setting needed to implement the arguments in [2004.05769]. It facilitates the study of various multiplet W-(super)algebras using the same geometric representation theory (Feigin-Tipunin construction), based only on relatively easy computation in the free-field algebra and a structure of the rank 1 case. As an application, we will extend almost all the main results of [2004.05769, 2105.00638] to the multiplet principal W-(super)algebras for non-simply-laced cases and osp(1|2n), respectively. We also discuss some connections with 3d (supersymmetric) quantum field theory and 3-manifold invariants. |