Branching laws for tensor modules over classical locally finite Lie algebras

摘要

Let and g' be isomorphic to any two of the Lie algebras gl(∞) sl(∞), sp(∞), and so(∞). Let M be a simple tensor g-module. We introduce the notion of an embedding g' ? g of general tensor type and derive branching laws for triples g' g, M, where g' ? g is an embedding of general tensor type. More precisely, since M is in general not semisimple as a g;-module, we determine the socle filtration of M over g;. Due to the description of embeddings of classical locally finite Lie algebras given by Dimitrov and Penkov in 2009, our results hold for all possible embeddings g' ? g unless g' = gl(∞).