Presentation slides: PDF
Abstract: In 1935, Fueter proved a theorem which allows to construct special solutions for a quaternionic predecessor of the Dirac operator. The idea was that one could start from arbitrary holomorphic functions and translate these into regular functions using a suitable power of the Laplace operator. This result has been generalised in Clifford analysis (a function theory for the Dirac operator) on several occasions, and it turns out that the Fueter theorem is a deep result which has connections with many other subjects such as representation theory and the rather recent slice monogenic theory. In this talk, we will explain how Fueter’s result can be proved using the conformal symmetries of the Dirac operator, which opens up the possibility to extend it to other invariant operators.