Higher-level affine wreath product algebras

TL;DR

This paper introduces new classes of algebras called higher-level affine wreath product and Frobenius Hecke algebras, expanding the algebraic framework with broad, unified constructions.

Contribution

It defines and studies these new algebra classes, generalizing existing structures like affine Hecke and Sergeev algebras within a unified framework.

Findings

Produced a broad range of new higher-level algebras

Special cases include higher-level analogues of known algebras

New algebraic structures appear to be novel

Abstract

We define and study two new classes of algebras, called higher-level affine wreath product algebras and higher-level affine Frobenius Hecke algebras. They depend on a Frobenius superalgebra and are defined, respectively, as path algebras of the higher-level affine wreath product category and higher-level affine Frobenius Hecke category. Our constructions produce a broad range of new higher-level algebras under a unified framework. Special cases include higher-level analogues of the degenerate affine Hecke algebra and affine Sergeev algebras, both of which appear to be new.