The $\hat W$-orbit of $ρ$, Kostant's formula for powers of the Euler product and affine Weyl groups as permutations of Z

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171150Let an affine Weyl group $\hat W$ act as a group of affine transformations on a real vector space V. We analyze the $\hat W$-orbit of a regular element in V and deduce applications to Kostant's formula for powers of the Euler product and to the representations of $\hat W$ as permutations of the integers.Latex, 27 pages, minor corrections, to appear in Journal of Pure and Applied AlgebraRepresentation TheoryCombinatoricsThe $\hat W$-orbit of $ρ$, Kostant's formula for powers of the Euler product and affine Weyl groups as permutations of Ztext