Affine wreath product algebras
arXiv:1709.02998 · doi:10.1093/imrn/rny092
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.
41 pages. v2: Small corrections, published version. v3: Correction of (5.13) and minor typos
References in corpus (9)
- Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras
- Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification
- Frobenius Heisenberg categorification
- Hilbert schemes, Hecke algebras and the Calogero-Sutherland system
- The Elliptic Hall algebra and the deformed Khovanov Heisenberg category
- Centers of degenerate cyclotomic Hecke algebras and parabolic category O
- A graphical calculus for the Jack inner product on symmetric functions
- Nested Frobenius extensions of graded superrings
- An isomorphism theorem for degenerate cyclotomic Yokonuma-Hecke algebras and applications
Cited by in corpus (13)
- Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification
- Frobenius Heisenberg categorification
- Foundations of Frobenius Heisenberg categories
- Quantum Frobenius Heisenberg categorification
- Presentations of linear monoidal categories and their endomorphism algebras
- String diagrams and categorification
- Frobenius nilHecke algebras
- Quantum affine wreath algebras
- Affine oriented Frobenius Brauer categories
- Group partition categories
- KLR and Schur algebras for curves and semi-cuspidal representations
- Frobenius W-algebras and traces of Frobenius Heisenberg categories
- Affine Frobenius Brauer Categories