Representations of the Dunkl total angular momentum algebra

Alexis Langlois-Rémillard (Ghent University)

Wednesday 15th February 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.

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