报告题目： Centralizers of su(2) actions and the Racah algebra
报告人：Professor Luc Vinet，Centre de Recherches Mathématiques，Université de Montréal
The universal centralizer for the addition of three su(2) is known as the Racah algebra and is generated by the set of Casimir elements. We investigate the centralizers of the direct product of three irreducible su(2) representations labelled by the integers or half- integers ji, i = 1, 2, 3. We shall offer and motivate a conjecture giving these centralizers as quotients of the Racah algebra under polynomial relations involving the generators of the latter. That specializations of the Temperley-Lieb and Brauer algebras are recovered in the special cases j1=j2=j3=1/2 and j1=j2=J3=1 respectively, will be observed. We shall also indicate that the conjecture holds for j1 arbitrary and j2=j3=1/2 in which case, remarkably, the centralizer is identified as a one-boundary Temperley-Lieb algebra. This talk is Based on work done in collaboration with Nicolas Crampé (CRM/Tours) and Loïc Poulain D’Andecy (Reims).
Luc Vinet is Aisenstadt Professor of Mathematical Physics at the Université de Montréal. He is a distinguished scientist whose work spans Gauge Theories, Algebraic Combinatorics, Representation Theory and Special Functions as well Quantum Information. He holds doctorates from the Université Pierre and Marie Curie in Paris and the Université de Montréal and has been a postdoctoral fellow at MIT. He has been Provost of McGill University and Rector of the Université de Montréal. He is a Fellow of the Royal Society of Canada and an Officer of the National Order of Quebec. He is also a Fellow of the American Mathematical Society. He has received many prizes and awards among them the CAP-CRM Medal for accomplishments in Theoretical and Mathematical Physics, the Armand-Frappier prize of Quebec and an honorary doctorate from the Université Claude-Bernard (Lyon). He has moreover been inducted in the Ordre de la Pléïade and decorated by the French Government. He is currently the Director of the CRM one of the elite institutes for mathematical research in the world.