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Transvectants, Rankin-Cohen brackets, conformally covariant bi-differential operators

Jean-Louis Clerc (Univ. - Lorraine)
Torsdag, 7 april, 2016, at 16:15, in Aud. D3 (1531-215)
After the introduction of the Omega-process by Cayley, the transvectants were an important tool in the classical theory of invariants during the second half of the XIXth century and beginning of the XXth. The Rankin-Cohen brackets, introduced first by Rankin in 1956 and extended by Cohen in 1975 play an important role in the theory of modular forms. It was realized quite late that transvectants and RC brackets were basically the same objects, but for different parameters.

I will give an elementary presentation of these notions, and explain that they are examples of covariant bi-differential operators for the group SL(2,R). I will then explain how to construct such operators in more general situations.
Kontaktperson: Bent Ørsted