@article{18154,
  abstract     = {In 1976, Deligne and Lusztig realized the representation theory of finite groups of Lie type inside étale cohomology of certain algebraic varieties. Recently, a p-adic version of this theory started to emerge: there are p-adic Deligne–Lusztig spaces, whose cohomology encodes representation theoretic information for p-adic groups – for instance, it partially realizes the local Langlands correspondence with characteristic zero coefficients. However, the parallel case of coefficients of positive characteristic  ℓ≠p has not been inspected so far. The purpose of this article is to initiate such an inspection. In particular, we relate cohomology of certain p-adic Deligne–Lusztig spaces to Vignéras's modular local Langlands correspondence for GLn.},
  author       = {Löwit, Jakub},
  issn         = {1090-266X},
  journal      = {Journal of Algebra},
  number       = {2},
  pages        = {81--118},
  publisher    = {Elsevier},
  title        = {{On modulo ℓ cohomology of p-adic Deligne–Lusztig varieties for GLn}},
  doi          = {10.1016/j.jalgebra.2024.08.033},
  volume       = {663},
  year         = {2025},
}

@article{18617,
  abstract     = {Any complex-valued polynomial on (Rn)k decomposes into an algebraic combination of O(n)-invariant polynomials and harmonic polynomials. This decomposition, separation of variables, is granted to be unique if n≥2k−1. We prove that the condition n≥2k−1 is not only sufficient, but also necessary for uniqueness of the separation. Moreover, we describe the structure of non-uniqueness of the separation in the boundary cases when n=2k−2 and n=2k−3.
Formally, we study the kernel of a multiplication map ϕ carrying out separation of variables. We devise a general algorithmic procedure for describing Ker ϕ in the restricted non-stable range k≤n<2k−1. In the full non-stable range n<2k−1, we give formulas for highest weights of generators of the kernel as well as formulas for its Hilbert series. Using the developed methods, we obtain a list of highest weight vectors generating Ker ϕ.},
  author       = {Beďatš, Daniel},
  issn         = {0021-8693},
  journal      = {Journal of Algebra},
  pages        = {281--304},
  publisher    = {Elsevier},
  title        = {{Separation of variables for scalar-valued polynomials in the non-stable range}},
  doi          = {10.1016/j.jalgebra.2024.04.013},
  volume       = {651},
  year         = {2024},
}

@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},
}