TL;DR
This paper investigates the structure and representation theory of affine wreath product algebras, unifying various important algebras in the literature and providing new results, including proofs of open conjectures.
Contribution
It introduces a comprehensive framework for affine wreath product algebras, unifying and generalizing many known algebras and proving new results.
Findings
Unified framework for affine wreath product algebras
Simplified proofs of known results
Proofs of two open conjectures of Kleshchev and Muth
Abstract
We study the structure and representation theory of affine wreath product algebras and their cyclotomic quotients. These algebras, which appear naturally in Heisenberg categorification, simultaneously unify and generalize many important algebras appearing in the literature. In particular, special cases include degenerate affine Hecke algebras, affine Sergeev algebras (degenerate affine Hecke-Clifford algebras), and wreath Hecke algebras. In some cases, specializing the results of the current paper recovers known results, but with unified and simplified proofs. In other cases, we obtain new results, including proofs of two open conjectures of Kleshchev and Muth.
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