On the Mackey formulas for cyclotomic Hecke algebras and categories O of rational Cherednik algebras

TL;DR

This paper proves Mackey formulas for tensor induction/restriction functors in cyclotomic Hecke algebras and categories O of rational Cherednik algebras, advancing understanding of their representation theory.

Contribution

It establishes Mackey formulas in two key algebraic settings involving cyclotomic Hecke algebras and rational Cherednik algebras, providing new tools for their analysis.

Findings

Mackey formulas for cyclotomic Hecke algebras established

Mackey formulas for categories O of rational Cherednik algebras proved

Enhanced understanding of induction and restriction functors in these contexts

Abstract

In this paper, we shall establish the Mackey formulas in the following two set ups: (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 among categories O of rational Cherednik algebras for the complex reflection group of type G(r, 1, n) and their parabolic subgroups.