A Fundamental Domain for the General Linear Group by Means of Successive Minima
Journal of Lie Theory, Tome 33 (2023) no. 3, pp. 845-873
Voir la notice de l'article provenant de la source Heldermann Verlag
We present a variant of the method of construction of Watanabe of a fundamental domain for the translation action by the subgroup of rational points on the whole group of adélic points of the general linear group over an arbitrary number field. The obtained domain is a generalization of Grenier's one, not Minkowski's. For several fields, we profit our presentation to show that the fundamental domain is in a so-called {Siegel} set. As an example, inequalities bounding our fundamental domain are explicitly determined in the case of degree 3 over the imaginary quadratic field with discriminant -3, which will be interesting to some people.
Classification :
11H55, 11H50, 20G35
Mots-clés : Fundamental domain, Ryshkov domain, general linear group
Mots-clés : Fundamental domain, Ryshkov domain, general linear group
Affiliations des auteurs :
Masami Fujimori 1
Masami Fujimori. A Fundamental Domain for the General Linear Group by Means of Successive Minima. Journal of Lie Theory, Tome 33 (2023) no. 3, pp. 845-873. http://geodesic.mathdoc.fr/item/JOLT_2023_33_3_a8/
@article{JOLT_2023_33_3_a8,
author = {Masami Fujimori},
title = {A {Fundamental} {Domain} for the {General} {Linear} {Group} by {Means} of {Successive} {Minima}},
journal = {Journal of Lie Theory},
pages = {845--873},
year = {2023},
volume = {33},
number = {3},
url = {http://geodesic.mathdoc.fr/item/JOLT_2023_33_3_a8/}
}