Zhengwei Liu gave a talk on "A new one-parameter centralizer algebra and higher Dynkin diagrams" at the MIT Mathematics Department on Friday, December 8 at 3:00 in 2-361 as part of the MIT Infinite Dimensional Algebra seminar series. Click the photo above to view more pictures from the seminar.
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.