Year: 2026
Type: preprint
Abstract: We define double affine Hecke algebras associated to the $\textrm{GL}_n$ and $\textrm{SL}_n$ root data, decorated by a supersymmetric Frobenius superalgebra. When the Frobenius algebra is the group algebra of a finite group, we obtain new double affine versions of the quantum wreath Hecke algebras, and in particular of the affine Yokonuma-Hecke algebras. We prove a basis theorem, describe the centre for generic parameters, and define polynomial representations. We also provide a diagrammatic interpretation, from which we deduce certain involutions and symmetries of the algebra, and use it to describe an $\textrm{SL}_2(\mathbb{Z})$-action by outer automorphisms.
Source: arXiv (Cornell University)
Author: Mattarei, Niccolò
Institution: University of Ottawa
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G4998900716
OpenAlex ID: W7222450033