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

Cellini, Paola; Frajria, Pierluigi Moseneder; Papi, Paolo

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

Authors

Cellini, Paola

Frajria, Pierluigi Moseneder

Papi, Paolo

Description

Let 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 Algebra