G. Syam Prasad

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1.1. A fake projective plane is a smooth compact complex surface which is not the complex projective plane but has the same Betti numbers as the complex projective plane. Such a surface is known to be projective algebraic and it is the quotient of the (open) unit ball B in C (B is the symmetric space of PU(2, 1)) by a torsion-free cocompact discrete(More)
  • STEPHEN DEBACKER, Robert Kottwitz’s, +4 authors Eng-Chye Tan
In his paper The characters of reductive -adic groups [14] Harish-Chandra outlines his philosophy about harmonic analysis on reductive -adic groups. According to this philosophy, there are two distinguished classes of distributions on the group: orbital integrals and characters. Similarly, there are two classes of distributions on the Lie algebra which are(More)
“In this remarkable book, David Easley and Jon Kleinberg bring all the tools of computer science, economics, and sociology to bear on one of the great scientific challenges of our time: understanding the structure, function, and dynamics of networks in society. Clearly written and covering an impressive range of topics, “Networks, Crowds, and Markets” is(More)
The paper was motivated by a question of Vilonen, and the main results have been used by Mirković and Vilonen to give a geometric interpretation of the dual group (as a Chevalley group over Z) of a reductive group. We define a quasi-reductive group over a discrete valuation ring R to be an affine flat group scheme over R such that (i) the fibers are of(More)
The goal of this paper is two-fold. First, we introduce and analyze a new relationship between (Zariski-dense) abstract subgroups of the group of F rational points of a connected semi-simple algebraic group defined over a field F , which we call weak commensurability. This relationship is expressed in terms of the eigenvalues of individual elements, and(More)
— We give a new proof of a useful result of Guy Rousseau on Galois-fixed points in the Bruhat-Tits building of a reductive group. Résumé (Points fixes de Galois dans l’immeuble de Bruhat-Tits d’un groupe réductif ) Nous donnons une nouvelle preuve d’un résultat utile de Guy Rousseau sur les points fixes de Galois dans l’immeuble de Bruhat-Tits d’un groupe(More)
We give a cohomological criterion for existence of outer automorphisms of a semisimple algebraic group over an arbitrary field. This criterion is then applied to the special case of groups of type D2n over a global field, which completes some of the main results from the paper “Weakly commensurable arithmetic groups and isospectral locally symmetric spaces”(More)