On BGG resolutions of unitary modules for quiver Hecke and Cherednik algebras

Bowman, C.; Norton, E.; Simental, J.

doi:10.1007/s00029-021-00739-x

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On BGG resolutions of unitary modules for quiver Hecke and Cherednik algebras

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Norton, E.
Max Planck Institute for Mathematics, Max Planck Society;

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Simental, J.
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00029-021-00739-x
(Publisher version)

https://doi.org/10.48550/arXiv.1803.08736
(Preprint)

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Citation

Bowman, C., Norton, E., & Simental, J. (2022). On BGG resolutions of unitary modules for quiver Hecke and Cherednik algebras. Selecta Mathematica, 28(2): 29. doi:10.1007/s00029-021-00739-x.

Cite as: https://hdl.handle.net/21.11116/0000-0009-B899-B

Abstract

We provide a homological construction of unitary simple modules of Cherednik and
Hecke algebras of type A via BGG resolutions, solving a conjecture of Berkesch–
Griffeth–Sam. We vastly generalize the conjecture and its solution to cyclotomic
Cherednik and Hecke algebras over arbitrary ground ﬁelds, and calculate the Betti
numbers and Castelnuovo–Mumford regularity of certain symmetric linear subspace
arrangements.