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

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

2005-07-29

arxiv.org/abs/math/0507610v2

J. Pure Appl. Algebra 208 (2007), no. 3, 1103--1119.

Mathematics

Representation Theory

Latex, 27 pages, minor corrections, to appear in Journal of Pure and Applied Algebra

Scientific paper

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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