Branching laws for tensor modules over classical locally finite Lie algebras

作者：Hristova Elitza^*

来源：Journal of Algebra, 2014, 397: 278-314.

DOI：10.1016/j.jalgebra.2013.08.035

• Locally finite Lie algebras
• Tensor modules
• Branching laws
• Socle filtration

Let g%26apos; and g be isomorphic to any two of the Lie algebras gl(infinity), sl(infinity), sp(infinity), and so(infinity). Let M be a simple tensor g-module. We introduce the notion of an embedding g%26apos; subset of g of general tensor type and derive branching laws for triples g%26apos;, g, M, where g%26apos; subset of g is an embedding of general tensor type. More precisely, since M is in general not semisimple as a g%26apos;-module, we determine the socle filtration of M over g%26apos;. 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%26apos; subset of g unless g%26apos; congruent to gl(infinity).

• 出版日期2014-1-1