Manchester Algebra Seminar - Alexis Langlois-Rémillard
| Dates: | 31 January 2023 |
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| Times: | 13:00 - 14:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, Current University students |
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Speaker: Alexis Langlois-Rémillard - U Ghent
Title: Representations of the Dunkl total angular momentum algebra
Abstract: 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 then use it to give a coarse classification of the irreducible representations. We finish with some closing words sketching how to refine the coarse classification to a full classification.
Tea and biscuits 12:45 in the foyer
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Frank Adams
Alan Turing Building
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