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

Chris Bowman; Emily Norton; José Simental

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arXiv · 2107.01190

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

Chris Bowman·Emily Norton·José Simental

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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.

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BibTeX RIS

Chris Bowman, Emily Norton, José Simental. 2021-07-02. Unitary representations of cyclotomic Hecke algebras at roots of unity: combinatorial classification and BGG resolutions. https://arxiv.org/abs/2107.01190

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