# Root systems in number fields

## Meeting Details

Abstract: We classify the types of root systems $R$ in the rings of integers of number fields $K$ such that the Weyl group $W(R)$ lies in the group $L(K)$ generated by $Aut(K)$ and multiplications by nonzero elements of $K$. We also classify the Weyl groups of roots systems of rank $n$ that are isomorphic to a subgroup of $L(K)$ for a number field $K$ of degree $n$ over the field $Q$ of rational numbers. This is a report on a joint work with Vladimir L. Popov (Steklov Institute, Moscow).