Representations of the Dunkl total angular momentum algebra

Alexis Langlois-Rémillard (Ghent University)

Wednesday 15th February, 2023 16:00-17:00 Maths 311B


The Dunkl total angular momentum algebra is the supercentraliser of the realisation of the orthosymplectic Lie superalgebra osp(1|2) present inside the tensor product of a rational Cherednik algebra and a Clifford algebra. Its representation theory changes according to the reflection group involved, the dimension of the space and a parameter function. In this talk, we focus on the four-dimensional case with the group being the product of two dihedral groups. There we can define a subalgebra admitting a triangular decomposition that captures the structure of the finite-dimensional representations of the whole algebra. We finish with some closing words sketching the full classification and possible links with the Dunkl angular momenta algebra.

Add to your calendar

Download event information as iCalendar file (only this event)