The Loop Hecke Algebra and Charge Conserving Yang-Baxter Operators

Explore the intricacies of the Loop Hecke Algebra and Charge Conserving Yang-Baxter Operators in this 50-minute conference talk by Eric Rowell at the Centre de recherches mathématiques (CRM). Delve into the Loop Braid Group LBn, the motion group of n free loops in S3, and its finite-dimensional quotients LHn. Examine the structure of these non-semisimple Loop Hecke Algebras through representations obtained from loop braided vector spaces. Investigate the charge-conserving property of the matrix R and its implications. Learn about the recent classification of charge conserving Yang-Baxter operators and their concise combinatorial description. Gain insights into the ongoing research on LBn representations and the connections between these mathematical concepts. This talk is part of the Workshop on Quantum symmetries: Tensor Categories, Topological quantum field theories, and Vertex algebras held in October-November 2022.