Rankin-Cohen Brackets and Invariant Theory

  • Authors:

  • Y. Choie;B. Mourrain;P. Solé

  • Affiliations:

  • Department of Math. POSTECH, Pohang, Korea. yjc@vision.postech.ac.kr;INRIA Sophia Route des Lucioles, 06 903 Sophia-Antipolis, France. mourrain@sophia.inria.fr;CNRS-I3S, ESSI, BP 145, Route des Colles, 06 903 Sophia-Antipolis, France.ps@essi.fr

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 2001

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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 iSL(2, C) is given.