Old and New on S1(2).
Let be a complex reductive Lie algebra and be any reductive in subalgebra. We call a -module bounded if the -multiplicities of are uniformly bounded. In this paper we initiate a general study of simple bounded -modules. We prove a strong necessary condition for a subalgebra to be bounded (Corollary 4.6), i.e. to admit an infinite-dimensional simple bounded -module, and then establish a sufficient condition for a subalgebra to be bounded (Theorem 5.1). As a result we are able to...
Positioned eco-grammar systems (PEG systems, for short) were introduced in our previous papers. In this paper we engage in a new field of research, the hierarchy of PEG systems, namely in the hierarchy of the PEG systems according to the number of agents presented in the environment and according to the number of types of agents in the system.