Time: April 8th 2015 (Wed) 12:50-13:40
Place: Room N-101
(ICU Science Hall, 1st Floor, North Wing)
Title: Clifford analysis in the quaternionic setting
Speaker: Dr. David Eelbode*
(Department of Information Science, University of Antwerpen, Belgium）
Abstract: Classical Clifford analysis is often described as a function theory for the Dirac operator, the first-order differential operator factorizing the Laplace (or wave) operator on a higher-dimensional vector space. Although this operator is in fact conformally invariant, it is mostly known as a spin-invariant operator (its polynomial null solutions, for example, can be used to introduce representation spaces for the spin group). In this lecture we will see how the classical Dirac equation behaves under a branching of this spin group to certain subgroups: when considering the unitary (respectively symplectic) group, one obtains the Hermitean (respectively quaternionic Hermitean) refinement of classical Clifford analysis on the Euclidean space.
* David Eelbode is the W.K. Clifford Prize winner of 2014.