Abstract
In this paper we show that the cyclotomic factors of the E n Coxeter polynomials depend only on the value of n mod 360 , and come exclusively from spherical subdiagrams.
Highlights
In this paper we show that the cyclotomic factors of the En Coxeter polynomials depend only on the value of n mod 360, and come exclusively from spherical subdiagrams
The Coxeter number hn is the order of the Coxeter element wn ∈ Wn, and its characteristic polynomial
The vanishing of En(ζk) only depends on the value of n mod k, so by Corollary 2.3 no new roots of unity can occur as zeros of En(x) for n > 182
Summary
In this paper we show that the cyclotomic factors of the En Coxeter polynomials depend only on the value of n mod 360, and come exclusively from spherical subdiagrams. This result explains why the spherical Coxeter polynomials Ei(x), 3 ≤ i ≤ 8, occur as factors of En(x).
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