{"intvolume":"       149","title":"Contravariant forms on Whittaker modules","publisher":"American Mathematical Society","publication_status":"published","isi":1,"ec_funded":1,"date_updated":"2023-08-04T11:11:47Z","abstract":[{"lang":"eng","text":"Let g be a complex semisimple Lie algebra. We give a classification of contravariant forms on the nondegenerate Whittaker g-modules Y(χ,η) introduced by Kostant. We prove that the set of all contravariant forms on Y(χ,η) forms a vector space whose dimension is given by the cardinality of the Weyl group of g. We also describe a procedure for parabolically inducing contravariant forms. As a corollary, we deduce the existence of the Shapovalov form on a Verma module, and provide a formula for the dimension of the space of contravariant forms on the degenerate Whittaker modules M(χ,η) introduced by McDowell."}],"quality_controlled":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_created":"2020-11-19T10:17:40Z","issue":"1","date_published":"2021-01-01T00:00:00Z","language":[{"iso":"eng"}],"external_id":{"isi":["000600416300004"],"arxiv":["1910.08286"]},"main_file_link":[{"url":"https://arxiv.org/abs/1910.08286","open_access":"1"}],"acknowledgement":"We would like to thank Peter Trapa for useful discussions, and Dragan Milicic and Arun Ram for valuable feedback on the structure of the paper. The first author acknowledges the support of the European Unions Horizon 2020 research and innovation programme under the Marie Skodowska-Curie Grant Agreement No. 754411. The second author is\r\nsupported by the National Science Foundation Award No. 1803059.","year":"2021","oa_version":"Preprint","publication_identifier":{"eissn":["1088-6826"],"issn":["0002-9939"]},"article_type":"original","month":"01","doi":"10.1090/proc/15205","article_processing_charge":"No","day":"01","author":[{"last_name":"Brown","id":"70B7FDF6-608D-11E9-9333-8535E6697425","first_name":"Adam","full_name":"Brown, Adam"},{"full_name":"Romanov, Anna","first_name":"Anna","last_name":"Romanov"}],"keyword":["Applied Mathematics","General Mathematics"],"_id":"8773","oa":1,"volume":149,"publication":"Proceedings of the American Mathematical Society","project":[{"name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"page":"37-52","citation":{"ista":"Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 149(1), 37–52.","ama":"Brown A, Romanov A. Contravariant forms on Whittaker modules. <i>Proceedings of the American Mathematical Society</i>. 2021;149(1):37-52. doi:<a href=\"https://doi.org/10.1090/proc/15205\">10.1090/proc/15205</a>","mla":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” <i>Proceedings of the American Mathematical Society</i>, vol. 149, no. 1, American Mathematical Society, 2021, pp. 37–52, doi:<a href=\"https://doi.org/10.1090/proc/15205\">10.1090/proc/15205</a>.","ieee":"A. Brown and A. Romanov, “Contravariant forms on Whittaker modules,” <i>Proceedings of the American Mathematical Society</i>, vol. 149, no. 1. American Mathematical Society, pp. 37–52, 2021.","chicago":"Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society, 2021. <a href=\"https://doi.org/10.1090/proc/15205\">https://doi.org/10.1090/proc/15205</a>.","short":"A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149 (2021) 37–52.","apa":"Brown, A., &#38; Romanov, A. (2021). Contravariant forms on Whittaker modules. <i>Proceedings of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/proc/15205\">https://doi.org/10.1090/proc/15205</a>"},"status":"public","department":[{"_id":"HeEd"}],"type":"journal_article"}