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arXiv · 1201.0032

Fake degrees for reflection actions on roots

Victor Reiner·Zhiwei Yun
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Abstract

A finite irreducible real reflection group of rank l and Coxeter number h has root system of cardinality h*l. It is shown that the fake degree for the permutation action on its roots is divisible by [h]_q = 1+q+q^2+...+q^{h-1}, and that in simply-laced types, it equals [h]_q times the summation of q^{e_i - 1} where e_i runs through the exponents, so that e_i - 1 are the codegrees.

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Victor Reiner, Zhiwei Yun. 2012-01-27. Fake degrees for reflection actions on roots. https://arxiv.org/abs/1201.0032

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