## Geometry Seminar - Abstracts

### Talk

Thursday 29 April 2021, 16:00-17:00 via zoom

**Quentin Labriet** (UniversitÃ© de Reims)

*Symmetry breaking operators and orthogonal polynomials*

### Abstract

Symmetry breaking operators are intertwinning operators for the restriction of an irreducible representation. In some cases, these are given by differential operators whose symbol is related some classical orthogonal polynomials. First, I willÂ describe the example of the Rankin-Cohen brackets which are symmetry breaking operators for the tensor product of two representation of the holomorphic discrete series of SL2(R). I will explain how they are related to Jacobi polynomials, and to the classical Jacobi transform. In a second part, I will discuss some ongoing work on the restriction for representation of the holomorphic discrete series for the conformal group of a tube domain.

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