2024/10/30 by Chih-Whi Chen, Chen, Chih-Whi, Shun‐Jen Cheng +3
Mathematics · #17B10 #17B20 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2410.22819
openalex publication_date 2024/10/30 · openalex created_date 2024/11/14 · openalex updated_date 2026/07/28
For a basic classical Lie superalgebra \mathfrak s, let \mathfrak g be the central extension of the Takiff superalgebra \mathfrak s⊗Λ(θ), where θ is an odd indeterminate. We study the category of \mathfrak g-Whittaker modules associated with a nilcharacter χ of \mathfrak g and show that it is equivalent to the category of \mathfrak s-Whittaker modules associated with a nilcharacter of \mathfrak s determined by χ. In the case when χ is regular, we obtain, as an application, an equivalence between the categories of modules over the supersymmetric finite W-algebras associated to the odd principal nilpotent element at non-critical levels and the category of the modules over the principal finite W-superalgebra associated to \mathfrak s. Here, a supersymmetric finite W-algebra is conjecturally the Zhu algebra of a supersymmetric affine W-algebra. This allows us to classify and construct irreducible representations of a principal finite supersymmetric W-algebra.