Journées SL2R à Reims 2018

Conformally covariant bi-differential operators for differential forms

18 oct. 2018, 14:00

50m

Amphi 2 (UFR Sciences)

Exposé

Orateur

Khalid Koufany (Université de Lorraine - Nancy)

Description

The classical Rankin-Cohen brackets are bi-differential operators from $C^{\mathrm{\infty }}(\mathbb{R})\times C^{\mathrm{\infty }}(\mathbb{R})$ into $C^{\mathrm{\infty }}(\mathbb{R})$. They are covariant for the diagonal action of $\mathrm{S}\mathrm{L}(2,\mathbb{R})$ through principal series representations. We construct generalizations of these operators, replacing $\mathbb{R}$ by ${\mathbb{R}}^n,$ the group $\mathrm{S}\mathrm{L}(2,\mathbb{R})$ by the group ${\mathrm{S}\mathrm{O}}_0(1,n+1)$ viewed as the conformal group of ${\mathbb{R}}^n,$ and functions by differential forms.