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Multidimensional Gauss reduction theory for conjugacy classes of $SL (n, ℤ)$

Oleg Karpenkov — 2013

Journal de Théorie des Nombres de Bordeaux

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

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Multidimensional Gauss reduction theory for conjugacy classes of SL ( n , ℤ )

Multidimensional Gauss reduction theory for conjugacy classes of $SL (n, ℤ)$