@article{11545,
  abstract     = {We classify contravariant pairings between standard Whittaker modules and Verma modules over a complex semisimple Lie algebra. These contravariant pairings are useful in extending several classical techniques for category O to the Miličić–Soergel category N . We introduce a class of costandard modules which generalize dual Verma modules, and describe canonical maps from standard to costandard modules in terms of contravariant pairings.
We show that costandard modules have unique irreducible submodules and share the same composition factors as the corresponding standard Whittaker modules. We show that costandard modules give an algebraic characterization of the global sections of costandard twisted Harish-Chandra sheaves on the associated flag variety, which are defined using holonomic duality of D-modules. We prove that with these costandard modules, blocks of category
N have the structure of highest weight categories and we establish a BGG reciprocity theorem for N .},
  author       = {Brown, Adam and Romanov, Anna},
  issn         = {0021-8693},
  journal      = {Journal of Algebra},
  keywords     = {Algebra and Number Theory},
  number       = {11},
  pages        = {145--179},
  publisher    = {Elsevier},
  title        = {{Contravariant pairings between standard Whittaker modules and Verma modules}},
  doi          = {10.1016/j.jalgebra.2022.06.017},
  volume       = {609},
  year         = {2022},
}

@article{6828,
  abstract     = {In this paper we construct a family of exact functors from the category of Whittaker modules of the simple complex Lie algebra of type  to the category of finite-dimensional modules of the graded affine Hecke algebra of type . Using results of Backelin [2] and of Arakawa-Suzuki [1], we prove that these functors map standard modules to standard modules (or zero) and simple modules to simple modules (or zero). Moreover, we show that each simple module of the graded affine Hecke algebra appears as the image of a simple Whittaker module. Since the Whittaker category contains the BGG category  as a full subcategory, our results generalize results of Arakawa-Suzuki [1], which in turn generalize Schur-Weyl duality between finite-dimensional representations of  and representations of the symmetric group .},
  author       = {Brown, Adam},
  issn         = {0021-8693},
  journal      = {Journal of Algebra},
  pages        = {261--289},
  publisher    = {Elsevier},
  title        = {{Arakawa-Suzuki functors for Whittaker modules}},
  doi          = {10.1016/j.jalgebra.2019.07.027},
  volume       = {538},
  year         = {2019},
}