Mikhail V. Belolipetsky

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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 arithmetic hyperbolic n-orbifold of the smallest volume. We give a formula for the Euler-Poincaré(More)
Let C be a oneor two-sided Kazhdan–Lusztig cell in a Coxeter group (W,S), and let Reduced(C) be the set of reduced expressions of all w ∈ C, regarded as a language over the alphabet S. Casselman has conjectured that Reduced(C) is regular. In this paper we give a conjectural description of the cells when W is the group corresponding to a hyperbolic polygon,(More)
An old but fundamental problem in the arithmetic theory of quadratic forms is the computation of the mass of a lattice L in a quadratic space (V, q) over a number field F . Among the pioneers of its study were Smith, Minkowski and Siegel. After the work of Kneser, Tamagawa and Weil, this problem can be neatly formulated in group theoretic terms. More(More)