The Category of reduced imaginary Verma modules

2023/07/10 by Juan Camilo Arias, Vyacheslav Futorny, Arias, Juan Camilo +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2307.04306

openalex publication_date 2023/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For an arbitrary affine Lie algebra we study an analog of the category O for the natural Borel subalgebra and zero central charge. We show that such category is semisimple having the reduced imaginary Verma modules as its simple objects. This generalizes the result of Cox, Futorny, Misra in the case of affine sl(2).

Related

• Imaginary Verma modules for the extended Affine Lie algebra sl₂(C_q)
• Imaginary highest-weight representation theory and symmetric functions
• Restriction to Levi subalgebras and generalization of the category O
• Representations of Affine and Toroidal Lie Algebras
• Category O for truncated current Lie algebras