[{"_id":"11545","file":[{"file_name":"2022_JournalAlgebra_Brown.pdf","success":1,"access_level":"open_access","relation":"main_file","file_size":582962,"date_updated":"2023-02-02T07:32:48Z","date_created":"2023-02-02T07:32:48Z","content_type":"application/pdf","file_id":"12473","creator":"dernst","checksum":"82abaee3d7837f703e499a9ecbb25b7c"}],"date_created":"2022-07-08T11:40:07Z","abstract":[{"lang":"eng","text":"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.\r\nWe 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\r\nN have the structure of highest weight categories and we establish a BGG reciprocity theorem for N ."}],"year":"2022","citation":{"mla":"Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” <i>Journal of Algebra</i>, vol. 609, no. 11, Elsevier, 2022, pp. 145–79, doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2022.06.017\">10.1016/j.jalgebra.2022.06.017</a>.","apa":"Brown, A., &#38; Romanov, A. (2022). Contravariant pairings between standard Whittaker modules and Verma modules. <i>Journal of Algebra</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jalgebra.2022.06.017\">https://doi.org/10.1016/j.jalgebra.2022.06.017</a>","short":"A. Brown, A. Romanov, Journal of Algebra 609 (2022) 145–179.","chicago":"Brown, Adam, and Anna Romanov. “Contravariant Pairings between Standard Whittaker Modules and Verma Modules.” <i>Journal of Algebra</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jalgebra.2022.06.017\">https://doi.org/10.1016/j.jalgebra.2022.06.017</a>.","ama":"Brown A, Romanov A. Contravariant pairings between standard Whittaker modules and Verma modules. <i>Journal of Algebra</i>. 2022;609(11):145-179. doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2022.06.017\">10.1016/j.jalgebra.2022.06.017</a>","ieee":"A. Brown and A. Romanov, “Contravariant pairings between standard Whittaker modules and Verma modules,” <i>Journal of Algebra</i>, vol. 609, no. 11. Elsevier, pp. 145–179, 2022.","ista":"Brown A, Romanov A. 2022. Contravariant pairings between standard Whittaker modules and Verma modules. Journal of Algebra. 609(11), 145–179."},"file_date_updated":"2023-02-02T07:32:48Z","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","title":"Contravariant pairings between standard Whittaker modules and Verma modules","publication_status":"published","article_type":"original","acknowledgement":"We thank Catharina Stroppel and Jens Niklas Eberhardt for interesting discussions. The first author acknowledges the support of the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. The second author is supported by the National Science Foundation Award No. 1803059 and the Australian Research Council grant DP170101579.","publication_identifier":{"issn":["0021-8693"]},"doi":"10.1016/j.jalgebra.2022.06.017","scopus_import":"1","publication":"Journal of Algebra","date_updated":"2023-08-03T11:56:30Z","ec_funded":1,"department":[{"_id":"HeEd"}],"intvolume":"       609","oa":1,"volume":609,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Brown","first_name":"Adam","full_name":"Brown, Adam","id":"70B7FDF6-608D-11E9-9333-8535E6697425"},{"full_name":"Romanov, Anna","last_name":"Romanov","first_name":"Anna"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"has_accepted_license":"1","project":[{"grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"}],"issue":"11","quality_controlled":"1","day":"01","page":"145-179","status":"public","month":"11","isi":1,"keyword":["Algebra and Number Theory"],"language":[{"iso":"eng"}],"ddc":["510"],"external_id":{"isi":["000861841100004"]},"date_published":"2022-11-01T00:00:00Z","type":"journal_article","publisher":"Elsevier"},{"oa":1,"volume":538,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"id":"70B7FDF6-608D-11E9-9333-8535E6697425","full_name":"Brown, Adam","first_name":"Adam","last_name":"Brown"}],"publication":"Journal of Algebra","date_updated":"2023-08-29T07:11:47Z","department":[{"_id":"HeEd"}],"intvolume":"       538","arxiv":1,"article_processing_charge":"No","oa_version":"Preprint","publication_status":"published","title":"Arakawa-Suzuki functors for Whittaker modules","article_type":"original","publication_identifier":{"issn":["0021-8693"]},"doi":"10.1016/j.jalgebra.2019.07.027","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1805.04676"}],"_id":"6828","date_created":"2019-08-22T07:54:13Z","abstract":[{"lang":"eng","text":"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 ."}],"year":"2019","citation":{"short":"A. Brown, Journal of Algebra 538 (2019) 261–289.","chicago":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” <i>Journal of Algebra</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.jalgebra.2019.07.027\">https://doi.org/10.1016/j.jalgebra.2019.07.027</a>.","apa":"Brown, A. (2019). Arakawa-Suzuki functors for Whittaker modules. <i>Journal of Algebra</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jalgebra.2019.07.027\">https://doi.org/10.1016/j.jalgebra.2019.07.027</a>","mla":"Brown, Adam. “Arakawa-Suzuki Functors for Whittaker Modules.” <i>Journal of Algebra</i>, vol. 538, Elsevier, 2019, pp. 261–89, doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2019.07.027\">10.1016/j.jalgebra.2019.07.027</a>.","ama":"Brown A. Arakawa-Suzuki functors for Whittaker modules. <i>Journal of Algebra</i>. 2019;538:261-289. doi:<a href=\"https://doi.org/10.1016/j.jalgebra.2019.07.027\">10.1016/j.jalgebra.2019.07.027</a>","ieee":"A. Brown, “Arakawa-Suzuki functors for Whittaker modules,” <i>Journal of Algebra</i>, vol. 538. Elsevier, pp. 261–289, 2019.","ista":"Brown A. 2019. Arakawa-Suzuki functors for Whittaker modules. Journal of Algebra. 538, 261–289."},"external_id":{"isi":["000487176300011"],"arxiv":["1805.04676"]},"date_published":"2019-11-15T00:00:00Z","type":"journal_article","publisher":"Elsevier","status":"public","month":"11","isi":1,"language":[{"iso":"eng"}],"quality_controlled":"1","day":"15","page":"261-289"}]