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Oleg Karpenkov
Multidimensional Gauss reduction theory for conjugacy classes of $\mathrm{SL}(n,\mathbb{Z})$
Journal de théorie des nombres de Bordeaux, 25 no. 1 (2013), p. 99-109, doi: 10.5802/jtnb.828
Article PDF | Reviews MR 3063833 | Zbl 1273.11111

Résumé - Abstract

In this paper we describe the set of conjugacy classes in the group ${\mathord {\rm SL}}(n,\mathbb{Z})$. We expand geometric Gauss Reduction Theory that solves the problem for ${\mathord {\rm SL}}(2,\mathbb{Z})$ to the multidimensional case, where $\varsigma $-reduced Hessenberg matrices play the role of reduced matrices. Further we find complete invariants of conjugacy classes in ${\mathord {\rm GL}}(n,\mathbb{Z})$ in terms of multidimensional Klein-Voronoi continued fractions.

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