Contravariant forms on Whittaker modules

A. Brown, A. Romanov, Proceedings of the American Mathematical Society 149 (2020) 37–52.


Journal Article | Epub ahead of print | English
Author
Brown, AdamIST Austria; Romanov, Anna
Department
Abstract
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.
Publishing Year
Date Published
2020-10-09
Journal Title
Proceedings of the American Mathematical Society
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 supported by the National Science Foundation Award No. 1803059.
Volume
149
Page
37-52
ISSN
eISSN
IST-REx-ID

Cite this

Brown A, Romanov A. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 2020;149:37-52. doi:10.1090/proc/15205
Brown, A., & Romanov, A. (2020). Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/proc/15205
Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society. American Mathematical Society, 2020. https://doi.org/10.1090/proc/15205.
A. Brown and A. Romanov, “Contravariant forms on Whittaker modules,” Proceedings of the American Mathematical Society, vol. 149. American Mathematical Society, pp. 37–52, 2020.
Brown A, Romanov A. 2020. Contravariant forms on Whittaker modules. Proceedings of the American Mathematical Society. 149, 37–52.
Brown, Adam, and Anna Romanov. “Contravariant Forms on Whittaker Modules.” Proceedings of the American Mathematical Society, vol. 149, American Mathematical Society, 2020, pp. 37–52, doi:10.1090/proc/15205.
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