2021/08/17 by Chih-Whi Chen, Chen, Chih-Whi
Mathematics · #17B10 #17B55 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2108.07532
openalex publication_date 2021/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend Kostant's result on annihilator ideals of non-singular simple Whittaker modules over Lie algebras to (possibly singular) simple Whittaker modules over Lie superalgebras. We describe these annihilator ideals in terms of certain primitive ideals coming from the category \mathcal O for quasireductive Lie superalgebras. To determine these annihilator ideals, we develop annihilator-preserving equivalences between certain full subcategories of the Whittaker category \mathcal N and the categories of certain projectively presentable modules in the category \mathcal O. These equivalences lead to a classification of simple Whittaker modules that lie in the integral central blocks when restricted to the even subalgebra. We make a connection between the linkage classes of integral blocks of \mathcal O and of \mathcal N. In particular, they can be computed via Kazhdan-Lusztig combinatorics for Lie superalgebras of type \mathfrakgl and \mathfrakosp. We then give a description of the integral blocks of the category \mathcal N of Whittaker modules for Lie superalgebras \mathfrakgl(m|n), \mathfrakosp(2|2n) and \mathfrakpe(n).