In collaboration with Mikhail Shkolnikov (algebraic geometry and topology group of Prof. Hausel), postdoc Enderalp Yakaboylu has shown that quantum particles interacting with a many-particle environment can be described using so-called “quantum groups” (or “q-deformed Lie algebras”). This provides an interesting new connection between condensed-matter physics and mathematics.
E. Yakaboylu, M. Shkolnikov, M. Lemeshko
Quantum groups as hidden symmetries of quantum impurities
Phys. Rev. Lett. 121, 255302 (2018), arXiv:1809.00222