A Note on Categorification and Spherical Harmonics

Using Khovanov’s categorification of the Weyl algebra, we investigate categorical structures arising from spherical harmonics. We categorify the s l ( 2 , 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 ∈ g l ( n , ℂ ) on the polynomial ring.