arXiv subjects

Salem Ben Saïd

Publications and source records attributed to Salem Ben Saïd.

2 recordsLinked to original sources

arXiv2023

The source operator method: an overview

This is an overview on the {source operator method} which leads to the construction of symmetry breaking differential operators (SBDO) in the context of tensor product of two principals series representations for the conformal group of a simple real Jordan algebra. This method can be applied to other geometric contexts: in the construction of SBDO for differential forms and for spinors, and also for the construction of Juhl's operators corresponding to the restriction from the sphere $S^n$ to $S^{n-1}$.

math.RT↗

arXiv2018

Conformally covariant bi-differential operators for differential forms

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

math.RT↗