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Higher spin algebras, Drinfel'd twists and Rankin-Cohen brackets
Mathematical Physics Seminar| Speaker: | Pierre Bieliavsky, Universite Catholique de Louvain |
| Location: | Zoom Room 975 4218 6104 Zoom-o-sphere |
| Start time: | Fri, Nov 20 2020, 11:00AM |
The aim of the talk is to present a close relation between certain algebras implied in higher spin theory and analytic number theory. Rankin-Cohen brackets are bi-differential operators on modular forms.Certain formal superpositions of these operators have been shown to define associative products on the algebra of modular forms [Eholzer, Cohen-Manin-Zagier, Connes-Moscovici].I'll present a result which asserts that the associative superpositions of Rankin-Cohen brackets coincide with the formal star products on the plane that are invariant under the linear action of SL(2,R). Within this context, Eholzer's product equals Moyal's product.I'll give an explicit formula for each of these star products in terms of an integral kernel. The proof of this result is an application to the special case of the Lie algebra of the affine Lie group ``ax+b" of a method - which I call the ``retract method"- that explicitly constructs the intertwiners between formal Drinfel'd twists sharing a common symmetry.
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