The Cayley-Dirac operator on oriented Grassmannians

by David Eelbode (University of Antwerp)

Location: Campus Sterre, Building S8, Classroom 3.2, Ghent
Time: Friday March 1, 2019 at 13:30

In his PhD thesis, Tim Janssens has studied a differential operator which we have dubbed the Cayley-Dirac operator, for the simple reason that it factorises the so-called Cayley-Laplace operator (which has been studied in the past). Much to our surprise, these operators nicely generalise some properties from the classical case (harmonic/Clifford analysis in one vector variable) to a new setting, in which one essentially considers a suitable oriented Grassmannian instead of a sphere as the underlying ‘basic manifold’. During this talk, we would like to highlight a few of these facts: we will start from the Howe duality for a certain function space, and see how far we can go with that.

This is joint work with Yasushi Homma and Tim Janssens.