(1) Department of Math, POSTECH, Pohang, Korea;(2) INRIA Sophia Route des Lucioles, 06 903 Sophia-Antipolis, France;(3) CNRS-I3S, ESSI, BP 145, Route des Colles, 06 903 Sophia-Antipolis, France
Abstract:
Using maps due to Ozeki and Broué-Enguehard between graded spaces of invariants for certain finite groups and the algebra of modular forms of even weight we equip these invariants spaces with a differential operator which gives them the structure of a Rankin-Cohen algebra. A direct interpretation of the Rankin-Cohen bracket in terms of transvectant for the group SL(2, C) is given.