Branching laws for tensor modules over classical locally finite Lie algebras

Abstract

Let g′ 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(∞).