Whittaker Modules for W type Cartan Lie superalgebras

2025/11/22 by Futorny, Vyacheslav, Tantubay, Santanu
Mathematics · #17B10 #17B15 #17B65 #17B66 #17B68 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2511.17995

openalex publication_date 2025/11/22 · openalex created_date 2025/11/27 · openalex updated_date 2026/07/28

Abstract

We consider the category of Whittaker modules for the Lie superalgebra W_m,n of vector fields on ℂ^(m|n). For any a∈ ℂ^m we show the equivalence between the blocks Ω_{\mathbf a}^\widetildeW_m,n of the category of (AW)_m,n-Whittaker modules with finite-dimensional Whittaker vector spaces and the category of finite-dimensional modules over certain Lie subsuperalgebra T_m,n of (AW)_m,n (and also of \mathfrakgl(m,n)). Then we apply the covering technique to study Whittaker W_m,n-modules and describe simple modules in the category Ω_{\mathbf a}^W_m,n of such modules with finite-dimensional Whittaker vector spaces and with non-singular \mathbf a.

Citations

• Harish-Chandra modules for map and affine Lie superalgebras
• Tensor modules over Witt superalgebras
• bounded weight modules over the Lie superalgebra of Cartan W-type
• Classification of simple strong Harish-Chandra W(m,n)-modules
• Simple weight modules with finite-dimensional weight spaces over Witt superalgebras
• The category of weight modules for symplectic oscillator Lie algebras
• Whittaker modules for the super-Virasoro algebras
• Whittaker categories for the Virasoro algebra
• Blocks and modules for Whittaker pairs
• Whittaker Modules for the Virasoro Algebra
• Whittaker Modules for Generalized Weyl Algebras

Related

• Whittaker categories and strongly typical Whittaker modules for Lie superalgebras
• Blocks and modules for Whittaker pairs
• A Whittaker category for the Symplectic Lie algebra
• Annihilator ideals and blocks of Whittaker modules over quasireductive Lie superalgebras
• bounded weight modules over the Lie superalgebra of Cartan W-type