Fake degrees for reflection actions on roots

Details Fake degrees for reflection actions on roots Fake degrees for reflection actions on roots

2011-12-29

arxiv.org/abs/1201.0032v2

Mathematics

Combinatorics

Added discussion of overlap with prior work by J. Stembridge

Scientific paper

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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