Multidimensional Gauss reduction theory for conjugacy classes of SL(n,)
Journal de Théorie des Nombres de Bordeaux, Volume 25 (2013) no. 1, pp. 99-109.

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.

Dans cet article, nous décrivons l’ensemble des classes de conjugaison dans le groupe SL (n,). Nous étendons la théorie de réduction de Gauss géométrique qui résout le problème pour SL (2,) au cas multidimensionnel, où les matrices de Hessenberg ς-réduites jouent le rôle de matrices réduites. Ensuite, nous trouvons des invariants complets des classes de conjugaison dans GL (n,) en termes fractions continues multidimensionnelles de Klein-Voronoi.

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DOI: 10.5802/jtnb.828
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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, Volume 25 (2013) no. 1, pp. 99-109. doi : 10.5802/jtnb.828. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.828/

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