Infinite Dimensional Algebra Seminar
Friday, December 08, 2017 at 3:00pm to 5:00pm
Zhengwei Liu (Harvard)
A new one-parameter centralizer algebra and higher Dynkin diagrams
We introduce a new one-parameter centralizer algebra as a Fourier cousin of the Birman-Wenzl-Murakami algebra and prove unitarity at roots of unity. We find a new type of Schur-Weyl duality between this centralizer algebra and two families of quantum subgroups. We construct its irreducible representations and compute their quantum dimensions in a closed form. Its Bratteli diagram gives two families of Dynkin diagrams for Ocneanu's higher representation theory.