## Branching laws for tensor modules over classical locally finite Lie algebras

- Given an embedding of a Lie algebra g' into a Lie algebra g and an irreducible g-module M, the branching problem is to determine the structure of M as a module over g'. In this thesis, we consider the case when both g' and g are classical locally finite Lie algebras (embeddings of such Lie algebras have been described by I. Dimitrov and I. Penkov) and M is a simple tensor g-module (the class of tensor modules has been introduced and studied in a series of papers by E. Dan-Cohen, I. Penkov, V. Serganova, and K. Styrkas). The goal of the thesis is to solve the branching problem for such triples g', g, and M. Since M is in general a not completely reducible 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 I. Dimitrov and I. Penkov, when g' is simple our result holds for all possible embeddings of g' into g.