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.
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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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Presented by: Vyjayanthi Chari
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Arunasalam, S., Ciappara, J., Nguyen, D.M.H. et al. A Note on Categorification and Spherical Harmonics. Algebr Represent Theor 23, 1285–1295 (2020). https://doi.org/10.1007/s10468-019-09886-4
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DOI: https://doi.org/10.1007/s10468-019-09886-4