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Double affine Frobenius Hecke algebras
Abstract
We define double affine Hecke algebras associated to the GLn and SLn 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 SL2(ℤ)-action by outer automorphisms.
Related
BibTeX
@misc{mattarei2026double,
title = {{Double affine Frobenius Hecke algebras}},
author = {Niccolò Mattarei},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22156},
eprint = {2610.22156},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22156},
}
RIS
TY - UNPB
TI - Double affine Frobenius Hecke algebras
AU - Niccolò Mattarei
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.22156
UR - https://arxiv.org/abs/2610.22156
AB - We define double affine Hecke algebras associated to the GL_n and 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 SL_2(ℤ)-action by outer automorphisms.
ER -