Unitary representations of cyclotomic Hecke algebras at roots of unity: 
combinatorial classification and BGG resolutions

Bowman, Chris; Norton, Emily; Simental, José

doi:10.1017/S147474802200055X

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Unitary representations of cyclotomic Hecke algebras at roots of unity: combinatorial classification and BGG resolutions

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Simental, José
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1017/S147474802200055X
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https://doi.org/10.48550/arXiv.2107.01190
(Preprint)

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Citation

Bowman, C., Norton, E., & Simental, J. (2024). Unitary representations of cyclotomic Hecke algebras at roots of unity: combinatorial classification and BGG resolutions. Journal of the Institute of Mathematics of Jussieu, 23(2), 557-608. doi:10.1017/S147474802200055X.

Cite as: https://hdl.handle.net/21.11116/0000-000C-9005-B

Abstract

We relate the classes of unitary and calibrated representations of cyclotomic Hecke algebras, and, in particular, we show that for the most important deformation parameters these two classes coincide. We classify these representations in terms of both multipartition combinatorics and as the points in the fundamental alcove under the action of an affine Weyl group. Finally, we cohomologically construct these modules via BGG resolutions.