Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification
| Autor: | Marco Mackaay, Alistair Savage |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Heisenberg algebra Categorification Mathematics::Number Theory 0102 computer and information sciences 01 natural sciences Mathematics::Category Theory FOS: Mathematics 20C08 (Primary) 18D10 19A22 (Secondary) 0101 mathematics Algebra over a field Representation Theory (math.RT) Mathematics::Representation Theory Hecke algebras Mathematics Diagrammatic calculus Discrete mathematics Ring (mathematics) Algebra and Number Theory Functor 010102 general mathematics Degenerate energy levels Cyclotomic quotients Monoidal category 16. Peace & justice 010201 computation theory & mathematics Mathematics - Representation Theory |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| DOI: | 10.48550/arxiv.1705.03066 |
| Popis: | We associate a monoidal category $\mathcal{H}^\lambda$ to each dominant integral weight $\lambda$ of $\widehat{\mathfrak{sl}}_p$ or $\mathfrak{sl}_\infty$. These categories, defined in terms of planar diagrams, act naturally on categories of modules for the degenerate cyclotomic Hecke algebras associated to $\lambda$. We show that, in the $\mathfrak{sl}_\infty$ case, the level $d$ Heisenberg algebra embeds into the Grothendieck ring of $\mathcal{H}^\lambda$, where $d$ is the level of $\lambda$. The categories $\mathcal{H}^\lambda$ can be viewed as a graphical calculus describing induction and restriction functors between categories of modules for degenerate cyclotomic Hecke algebras, together with their natural transformations. As an application of this tool, we prove a new result concerning centralizers for degenerate cyclotomic Hecke algebras. Comment: 35 pages; v2: published version |
| Databáze: | OpenAIRE |
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