In this work the author lets $Phi$ be an irreducible root system, with Coxeter group $W$. He considers subsets of $Phi$ which are abelian, meaning that no two roots in the set have sum in $Phi cup { 0 }$. He classifies all maximal abelian sets (i.e., abelian sets properly contained in no other) up to the action of $W$: for each $W$-orbit of maximal abelian sets we provide an explicit representative $X$, identify the (setwise) stabilizer $W_X$ of $X$ in $W$, and decompose $X$ into $W_X$-orbits. Abelian sets of roots are closely related to abelian unipotent subgroups of simple algebraic...
In this work the author lets $Phi$ be an irreducible root system, with Coxeter group $W$. He considers subsets of $Phi$ which are abelian, meaning tha...
