article published yes Adam Brown author 70B7FDF6-608D-11E9-9333-8535E6697425 Anna Romanov author HeEd department ISTplus - Postdoctoral Fellowships project 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. American Mathematical Society2021 eng Applied MathematicsGeneral Mathematics 0002-9939 1088-6826 1910.08286 00060041630000410.1090/proc/15205 149137-52 Brown A, Romanov A. 2021. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 149(1), 37–52. A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149 (2021) 37–52. 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>. 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>. 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> 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> 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. 87732020-11-19T10:17:40Z2025-04-14T07:43:50Z