Outputs (5)

Counting maximal arithmetic subgroups (2007)
Journal Article
Belolipetsky, M., Ellenberg, J., & Venkatesh, A. (2007). Counting maximal arithmetic subgroups. Duke Mathematical Journal, 140(1), 1-33. https://doi.org/10.1215/s0012-7094-07-14011-0

We study the growth rate of the number of maximal arithmetic subgroups of bounded covolumes in a semisimple Lie group using an extension of the method developed by Borel and Prasad.

Finite groups and hyperbolic manifolds (2005)
Journal Article
Belolipetsky, M., & Lubotzky, A. (2005). Finite groups and hyperbolic manifolds. Inventiones Mathematicae, 162(3), 459-472. https://doi.org/10.1007/s00222-005-0446-z

The isometry group of a compact n-dimensional hyperbolic manifold is known to be finite. We show that for every n≥2, every finite group is realized as the full isometry group of some compact hyperbolic n-manifold. The cases n=2 and n=3 have been prov... Read More about Finite groups and hyperbolic manifolds.

A bound for the number of automorphisms of an arithmetic Riemann surface (2005)
Journal Article
Belolipetsky, M., & Jones, G. (2005). A bound for the number of automorphisms of an arithmetic Riemann surface. Mathematical Proceedings of the Cambridge Philosophical Society, 138(2), 289-299. https://doi.org/10.1017/s0305004104008035

We show that for every g > 1 there is a compact arithmetic Riemann surface of genus g with at least 4(g-1)automorphisms, and that this lower bound is attained by infinitely many genera, the smallest being 24.

On volumes of arithmetic quotients of SO(1, n) (2004)
Journal Article
Belolipetsky, M. (2004). On volumes of arithmetic quotients of SO(1, n). Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 3(4), 749-770

We apply G. Prasad's volume formula for the arithmetic quotients of semi-simple groups and Bruhat-Tits theory to study the covolumes of arithmetic subgroups of SO(1,n). As a result we prove that for any even dimension n there exists a unique compact... Read More about On volumes of arithmetic quotients of SO(1, n).

Cells and representations of right-angled Coxeter groups (2004)
Journal Article
Belolipetsky, M. (2004). Cells and representations of right-angled Coxeter groups. Selecta Mathematica (New Series), 10(3), 325-339. https://doi.org/10.1007/s00029-004-0355-9

We study Kazhdan–Lusztig cells and the corresponding representations of right-angled Coxeter groups and Hecke algebras associated to them. In case of the infinite groups generated by reflections in the hyperbolic plane about the sides of right-angled... Read More about Cells and representations of right-angled Coxeter groups.