# Clifford Research Group

## Seminars Academic year 2007-2008

- Monday 22-10-2007

David Eelbode

*The Rarita-Schwinger operator in Clifford analysis*

#### The Rarita-Schwinger operator in Clifford
analysis

David Eelbode (UGent)

*Abstract:*

Clifford analysis is most widely known as a well-developed tool for studying the Dirac operator from a function theoretical point of view. There are however other, more general, SO(m)-invariant differential operators which can be studied within the framework of Clifford analysis. The aim of our lecture is to define the so-called symmetric analogues of the RS-operator, which are a family of invariant differential operators acting between functions taking values in the space of monogenic polynomials.

Using elementary notions from representation theory, we will first construct the RS-operator and the twistor operator using the so-called twisted Dirac operator acting on spinor-valued one-forms. Afterwards, we will explain how to relate these operators to differential operators acting on functions in several vector variables, and give some results regarding the solution spaces for these operators.

[this seminar serves as a preparation for a seminar by dr. P. Van Lancker, scheduled for later this year]