Some Remarks about the Interaction Between Quantum Algebra and Representation Stability

Tensor categories are ubiquitous in modern mathematics. We will explore how they arise from the perspective of topological quantum computing. Despite their importance, it is hard to do explicit computations inside tensor categories. This is because we don't know how to compute 6j symbols, which are a coordinate representation of the associator. We compute some new 6j symbols and give applications to representation stability and the representation theory of affine braid groups.PhDMathematicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/138525/1/barter_1.pd