The category of weight modules for symplectic oscillator Lie algebras

2019/08/13 by Genqiang Liu, Kaiming Zhao, Liu, Genqiang +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1908.04534

Abstract

The rank n symplectic oscillator Lie algebra \mathfrakg_n is the semidirect product of the symplectic Lie algebra \mathfraksp_2n and the Heisenberg Lie algebra H_n. In this paper, we study weight modules with finite dimensional weight spaces over \mathfrakg_n. When z≠ 0, it is shown that there is an equivalence between the full subcategory O_\mathfrakg_n[ z] of the BGG category O_\mathfrakg_n for \mathfrakg_n and the BGG category O_\mathfraksp_2n for \mathfraksp_2n. Then using the technique of localization and the structure of generalized highest weight modules, we also give the classification of simple weight modules over \mathfrakg_n with finite-dimensional weight spaces.

Citations

• Classification of simple weight modules over affine Lie algebras
• Classification of Irreducible Nonzero Level Modules with Finite-Dimensional Weight Spaces for Affine Lie Algebras

Cited by

• Whittaker Modules for W type Cartan Lie superalgebras

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