The Loop Hecke Algebra and Charge Conserving Yang–Baxter Operators

Speaker: Eric Rowell

Date:    2022.11.30

Time:    9:30-11:00 am

Zoom: 537 192 5549    Passcode: BIMSA



The Loop Braid Group 𝐿𝐵𝑛 is the motion group of 𝑛 free loops in 𝑆3, with generators the “leapfrog” motions and the symmetric exchanges. In recent work with Celeste Damiani and Paul Martin, we defined a family of finite dimensional quotients 𝐿𝐻𝑛 of 𝐿𝐵𝑛 via certain quadratic relations. The structure of these (non-semisimple) Loop Hecke Algebras is partially understood through (conjecturally faithful) representations obtained from a loop braided vector space, i.e. a pair (𝑆, 𝑅) of Yang–Baxter operators satisfying the appropriate mixed relations. One salient feature of the matrix 𝑅 is that it is charge conserving. This begs the question: can we classify charge conserving Yang–Baxter operators? Recently with Martin, we have found such a classification with a concise combinatorial description. In this talk, I will give an overview of these two projects. Time permitting we will circle back to the question of 𝐿𝐵𝑛 representations.



[BIMSA-Tsinghua Quantum Symmetry Seminar]