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January 2021 On the Mackey formulas for cyclotomic Hecke algebras and categories $\mathcal{O}$ of rational Cherednik algebras
Toshiro Kuwabara, Hyohe Miyachi, Kentaro Wada
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Osaka J. Math. 58(1): 103-134 (January 2021).

Abstract

In this paper, we shall establish the Mackey formulas in the following two setups: (i) on the tensor induction and restriction functors on the modules over cyclotomic Hecke algebras (Ariki-Koike algebras) and their standard subalgebras of parabolic subgroups; (ii) on the Bezrukavnikov-Etingof induction and restriction functors [3] among categories $\mathcal{O}$ [11] of rational Cherednik algebras for the complex reflection group of type $G(r,1,n)$ and their parabolic subgroups.

Acknowledgments

The authors would like to thank Seth Shelley-Abrahamson for letting us notice their paper [16]. There were some overlaps between [loc. cit.] and the original version of this paper. The authors would like to thank the referee for his or her effort to make this paper more readable. The first author was supported by JSPS KAKENHI Grant Number JP17K14151. The second author was supported by JSPS KAKENHI Grant Number JP18K03250. The third author was supported by JSPS KAKENHI Grant Number JP16K17565.

Citation

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Toshiro Kuwabara. Hyohe Miyachi. Kentaro Wada. "On the Mackey formulas for cyclotomic Hecke algebras and categories $\mathcal{O}$ of rational Cherednik algebras." Osaka J. Math. 58 (1) 103 - 134, January 2021.

Information

Received: 2 November 2018; Revised: 13 September 2019; Published: January 2021
First available in Project Euclid: 9 May 2021

Subjects:
Primary: 20C08
Secondary: 20F36, 20G05

Rights: Copyright © 2021 Osaka University and Osaka City University, Departments of Mathematics

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Vol.58 • No. 1 • January 2021
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