Elliptic complex reflection groups and Seiberg–Witten integrable systems

Abstract: For any abelian variety $X$ with an action of a finite complex reflection group $W$, Etingof, Felder, Ma and Veselov constructed a family of integrable systems on $T^*X$. When $X$ is a product of $n$ copies of an elliptic curve $E$ and $W=S_n$, this reproduces the usual elliptic Calogero­­-Moser system. Recently, together with Philip Argyres (Cincinnati) and Yongchao Lü (KIAS), we proposed that many of these integrable systems at the classical level can be interpreted as Seiberg­­-Witten integrable systems of certain super­symmetric quantum field theories. I will describe our progress in understanding this connection for the case $X=E^n$ where $E$ is an elliptic curve with the symmetry group $Z_m$ (of order $m=2,3,4,6$), and $W$ is the wreath product of $Z_m$ and $S_n$. I will mostly talk about $n=1$ case, which is already rather interesting. Based on: arXiv 2309.12760.

mathematical physicsdynamical systemsquantum algebrarepresentation theorysymplectic geometry

Audience: general audience

( slides | video )

---

BIMSA Integrable Systems Seminar

Series comments: The aim is to bring together experts in integrable systems and related areas of theoretical and mathematical physics and mathematics. There will be research presentations and overview talks.

Audience: Graduate students and researchers interested in integrable systems and related mathematical structures, such as symplectic and Poisson geometry and representation theory.

The zoom link will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.

---