Abstract
We study the monodromy of the Bezrukavnikov-Etingof induction and restriction functors for rational Cherednik algebras of type G(ℓ,1,n). We show that these produce an \(\mathfrak{sl}\)-categorification on the category \(\mathcal{O}\)’s for these algebras, and that, through the KZ-functor, it is compatible with a corresponding categorification on cyclotomic Hecke algebra representations.
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Acknowledgements
A lot of thanks go to Peng Shan, for many useful discussions spread over a long time. We would also like to thank Ivan Losev for helpful conversations. The first author is grateful for the financial support of EPSRC grant EP/G007632, and also for the hospitality of the Hausdorff Institute for Mathematics in Bonn and ETH in Zürich, where the final writing was completed.
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To Professor Jimbo, with admiration.
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Gordon, I.G., Martino, M. (2013). Monodromy of Partial KZ Functors for Rational Cherednik Algebras. In: Iohara, K., Morier-Genoud, S., Rémy, B. (eds) Symmetries, Integrable Systems and Representations. Springer Proceedings in Mathematics & Statistics, vol 40. Springer, London. https://doi.org/10.1007/978-1-4471-4863-0_6
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DOI: https://doi.org/10.1007/978-1-4471-4863-0_6
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