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Affine wreath product algebras

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arxiv 1709.02998 v3 pith:5QWNVIHB submitted 2017-09-09 math.RT math.RA

Alistair Savage This is my paper · ORCID
classification math.RTmath.RA
keywords algebrasaffinecasesresultswreathdegenerateheckeproduct
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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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  1. Higher-level degenerate spin affine Hecke superalgebras

    math.RT 2026-07 accept novelty 5.5 of 10

    Higher-level degenerate spin affine Hecke superalgebras are isomorphic (after Clifford tensor) to higher-level degenerate affine Hecke–Clifford superalgebras, hence Morita superequivalent.

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