On Hecke and asymptotic categories for a family of complex reflection groups

TL;DR

This paper generalizes the construction of Hecke algebras and categories, along with their asymptotic versions, for complex reflection groups G(M,M,N), extending known dihedral cases.

Contribution

It introduces a new framework for Hecke and asymptotic categories associated with complex reflection groups G(M,M,N), broadening the scope beyond dihedral groups.

Findings

Constructed Hecke algebras for G(M,M,N).

Proposed a strategy for Hecke categories construction.

Outlined asymptotic counterparts for these categories.

Abstract

Generalizing the dihedral picture for G(M,M,2), we construct Hecke algebras (and present a strategy for constructing Hecke categories) and asymptotic counterparts. We think of these as associated with the complex reflection group G(M,M,N).