A Note on Categorification and Spherical Harmonics

Arunasalam, Suntharan; Ciappara, Joshua; Nguyen, Diana M. H.; Tan, Suo Jun; Yacobi, Oded

doi:10.1007/s10468-019-09886-4

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2021

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“…This category is obtained as a certain category of modules over cohomology rings of infinite Grassmannianns and their Koszul duals. Categorification of Verma modules appeared independently in the litterature with a strongly different flavor in [12] and in [5].…”

Section: Introductionmentioning

confidence: 99%

2-Verma modules

Naisse¹,

Vaz²

2017

Preprint

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We construct a categorification of parabolic Verma modules for symmetrizable Kac-Moody algebras using KLR-like diagrammatic algebras. We show that our construction arises naturally from a dg-enhancement of the cyclotomic quotients of the KLR-algebras. As a consequence, we are able to recover the usual categorification of integrable modules. We also introduce a notion of dg-2-representation for quantum Kac-Moody algebras, and in particular of parabolic 2-Verma module.

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Section: Introductionmentioning

confidence: 99%

2-Verma modules

Naisse¹,

Vaz²

2017

Preprint

View full text Add to dashboard Cite

show abstract

2-Verma modules

Naisse

Vaz

2021

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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We construct a categorification of parabolic Verma modules for symmetrizable Kac–Moody algebras using KLR-like diagrammatic algebras. We show that our construction arises naturally from a dg-enhancement of the cyclotomic quotients of the KLR-algebras. As a consequence, we are able to recover the usual categorification of integrable modules. We also introduce a notion of dg-2-representation for quantum Kac–Moody algebras, and in particular of parabolic 2-Verma modules.

show abstract

A Note on Categorification and Spherical Harmonics

Cited by 2 publications

References 5 publications

2-Verma modules

2-Verma modules

2-Verma modules

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