Generalized Harish-Chandra Modules: A New Direction

الأصل · EN

Let g be a reductive Lie algebra over C. We say that a g-module M is a generalized Harish-Chandra module if, for some subalgebra k ⊂ g, M is locally k-finite and has finite k-multiplicities. We believe that the problem of classifying all irreducible generalized Harish-Chandra modules could be tractable. In this paper, we review the recent success with the case when k is a Cartan subalgebra. We also review the recent determination of which reductive in g subalgebras k are essential to a classification. Finally, we present in detail the emerging picture for the case when k is a principal 3-dimensional subalgebra.