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A Note on Categorification and Spherical Harmonics

  • Suntharan Arunasalam
  • Joshua CiapparaEmail author
  • Diana M. H. Nguyen
  • Suo Jun Tan
  • Oded Yacobi
Article
  • 13 Downloads

Abstract

Using Khovanov’s categorification of the Weyl algebra, we investigate categorical structures arising from spherical harmonics. We categorify the \(\mathfrak {s}\mathfrak {l}(2,\mathbb {C})\)-action on the polynomial ring in n variables, and use this to categorify certain simple Verma modules. On the way we also categorify the standard action of matrix units \(E_{ij}\in \mathfrak {g}\mathfrak {l}(n,\mathbb {C})\) on the polynomial ring.

Keywords

Spherical harmonics Categorification Verma modules 

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Notes

Acknowledgments

This research was undertaken in 2015 as part of a six-week undergraduate summer research project organised at the University of Sydney. D.N., S.T. and S.A. acknowledge support from the School of Mathematics at the University of Sydney through the 2014/15 Vacation Research Scholarship. J.C.’s Vacation Research Scholarship was funded by the Australian Mathematical Sciences Institute. O.Y. acknowledges support from the Australian Research Council.

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of PhysicsUniversity of SydneyCamperdownAustralia
  2. 2.School of Mathematics and StatisticsUniversity of SydneyCamperdownAustralia
  3. 3.Mathematical Sciences InstituteAustralian National UniversityAustralian Capital TerritoryAustralia

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