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

Paola Cellini·Pierluigi Moseneder Frajria·Paolo Papi
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Abstract

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.

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Paola Cellini, Pierluigi Moseneder Frajria, Paolo Papi. 2006-04-08. The $\hat W$-orbit of $ρ$, Kostant's formula for powers of the Euler product and affine Weyl groups as permutations of Z. https://arxiv.org/abs/math/0507610

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