Let R be a ring generated by l elements with stable range r. Assume that the group EL d (R) has Kazhdan constant ǫ 0 > 0 for some d ≥ r + 1. We prove that there exist ǫ(ǫ 0 , l) > 0 and k ∈ N, s.t. for every n ≥ d, EL n (R) has a generating set of order k and a Kazhdan constant larger than ǫ. As a consequence, we obtain for SL n (Z) where n ≥ 3, a Kazhdan constant which is independent of n w.r....

*This research has been partially supported by the National Science Foundation under grant IP~I-9120788, by the DARPA Basic Research Program under grant N00O14-92-J-1929, by the Army Research Office under contract DAAL03-91-C-0034 through Batelle Corporation, and by the Army Research Institute under contract MDA-903-92-R-0035 through Microelectronics and Design, Inc. Language-to-Language (L-L) ...

Let F be a non-archimedean local field with odd residual characteristic. Let G be the group SL2(F ). We construct explicit Whittaker models for any supercuspidal representation of G with positive level.

Let $S(G)$ be the Seidel matrix of a graph $G$ of order $n$ and let $D_S(G)=diag(n-1-2d_1, n-1-2d_2,ldots, n-1-2d_n)$ be the diagonal matrix with $d_i$ denoting the degree of a vertex $v_i$ in $G$. The Seidel Laplacian matrix of $G$ is defined as $SL(G)=D_S(G)-S(G)$ and the Seidel signless Laplacian matrix as $SL^+(G)=D_S(G)+S(G)$. The Seidel signless Laplacian energy $E_{SL^+...

We classify the real and strongly real conjugacy classes in GLnðqÞ and SLnðqÞ. In each case we give a formula for the number of real, and the number of strongly real, conjugacy classes. This paper is the first of two that together classify the real and strongly real classes in GLnðqÞ, SLnðqÞ, PGLnðqÞ, PSLnðqÞ, and all quasi-simple covers of PSLnðqÞ.

We give counterexamples to a version of the simple loop conjecture in which the target group is PSL(2,C). These examples answer a question of Minsky in the negative.