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

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 , ) . We expand geometric Gauss Reduction Theory that solves the problem for SL ( 2 , ) 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 , ) in terms of multidimensional Klein-Voronoi continued fractions.

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