Ladder Operators and Rational Extensions

This note presents the classification of ladder operators corresponding to the class of rational extensions of the harmonic oscillator. We show that it is natural to endow the class of rational extensions and the corresponding intertwining operators with the structure of a category REXT. The combinatorial data for this interpretation is realized as a functor MD -$>$ REXT, where MD refers to the set of Maya diagrams appropriately endowed with categorical structure. Our formalism allows us to easily reproduce and extend earlier results on ladder operators.