Generalized permutation matrices and non-weight modules over \mathfraksl(m|1)

2025/10/27 by Dimitrov, Ivan, Nguyen, Khoa, Paquette, Charles +1
#17A70 #17B10 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2510.22877

Abstract

We study the category M_\mathfraksl(m|1)(k|k) of \mathcal U(\mathfrak h)-free \mathcal U(\mathfraksl(m|1))-modules of rank k in each parity (rank (k|k)), where k∈ℤ_≥1. We construct an explicit family of such modules, provide an isomorphism theorem, and establish an indecomposability criterion.

Citations

• Bounded weight modules for basic classical Lie superalgebras at infinity
• A family of simple non-weight modules over the twisted N=2 superconformal algebra
• A family of simple non-weight modules over the twisted N = 2 superconformal algebra
• On non-weight representations of the N = 2 superconformal algebras
• Construction of simple non-weight sl(2)-modules of arbitrary rank

Related

• On U(\mathfrakh)-free modules over \mathfraksl(m|n)
• Non-weight modules over a Schrödinger-Virasoro type algebra
• A class of non-weight modules over the super-BMS₃ algebra
• Construction of simple non-weight sl(2)-modules of arbitrary rank
• Resolving Irreducible ℂS_n-Modules by Modules Restricted from GL_n(ℂ)