2017/05/11 by Michael Lau, Lau, Michael
Mathematics · #17B10 (primary) #17B22 (secondary) #17B65 #17B67 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1705.03989
openalex publication_date 2017/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For any reductive Lie algebra \mathfrakg and commutative, associative, unital algebra S, we give a complete classification of the simple weight modules of \mathfrakg⊗ S with finite weight multiplicities. In particular, any such module is parabolically induced from a simple admissible module for a Levi subalgebra. Conversely, all modules obtained in this way have finite weight multiplicities. These modules are isomorphic to tensor products of evaluation modules at distinct maximal ideals of S. Our results also classify simple Harish-Chandra modules up to isomorphism for all central extensions of current algebras.