Abstract
The goal of this article is to study the structure and representation theory of affine wreath product algebras and its cyclotomic quotients
These algebras appear naturally in Heisenberg categorification and generalize many important algebras (degenerate affine Hecke algebras, affine Sergeev algebras and wreath Hecke algebras). The whole class was introduced by D. Rosso and A. Savage in [Citation16]. In [Citation19], Savage studied both structure and representations under the condition that the trace map of A is even. In this paper we extend the definition for the case of odd trace. Since our approach is analogous to Savage’s, we consider the trace map being of arbitrary parity and unify statements and proofs. We also use an approach based on string diagrams, in the spirit of [Citation5]. For simplicity of exposition, we assume A to be symmetric.
2020 Mathematics subject classifications:
Acknowledgement
I would like to thank Alistair Savage and Iryna Kashuba, for their guidance throughout the project and for helpful comments that improved the paper.