The Loop Hecke Algebra and Charge Conserving Yang-Baxter Operators

Explore advanced mathematical concepts in this 48-minute seminar talk from the BIMSA-Tsinghua Quantum Symmetry Series, where Professor Eric Rowell from Texas A&M University delves into the Loop Braid Group and its finite dimensional quotients. Learn about the motion group of n free loops in S3, including leapfrog motions and symmetric exchanges, while discovering the structure of non-semisimple Loop Hecke Algebras through loop braided vector space representations. Examine the classification of charge conserving Yang-Baxter operators and their combinatorial descriptions, with insights into LBn representations. Gain deep mathematical understanding through referenced works, including forthcoming publications in the Pacific Journal of Mathematics and ongoing collaborative research with Martin, Damiani, and Torzewska.