Unramified reciprocal polynomials and Coxeter decompositions. (English) Zbl 1136.11313

Summary: We classify certain automorphisms of an even unimodular lattice \(L\) with fixed irreducible and unramified characteristic polynomial. The question which automorphisms are conjugate to their inverses in the orthogonal group of \(L\) is investigated.


11H56 Automorphism groups of lattices
11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
20F55 Reflection and Coxeter groups (group-theoretic aspects)