Limit multiplicities for principal congruence subgroups of GL(n). preprint

Abstract. We study the limiting behavior of the discrete spectra associated to the principal congruence subgroups of a reductive group over a number field. While this problem is well understood in the cocompact case (i.e. when the group is anisotropic modulo the center), we treat groups of unbounded rank. For the groups GL(n) we are able to show that the spectra converge to the Plancherel measure (the limit multiplicity property), and in general we obtain a substantial reduction of the problem. Our main tool is the recent refinement of the spectral side of Arthur’s trace formula obtained in [27, 25], which allows us to show that for GL(n) the contribution of the continuous spectrum is negligible in the limit. Content