We study the limiting behavior of the discrete spectra associated to theprincipal congruence subgroups of a reductive group over a number field. Whilethis problem is well understood in the cocompact case (i.e., when the group isanisotropic modulo the center), we treat groups of unbounded rank. For thegroups GL(n) and SL(n) we show that the suitably normalized spectra converge tothe Plancherel measure (the limit multiplicity property). For general reductivegroups we obtain a substantial reduction of the problem. Our main tool is therecent refinement of the spectral side of Arthur's trace formula obtained in[FLM11, FL11], which allows us to show that for GL(n) and SL(n) thecontribution of the continuous spectrum is negligible in the limit.
展开▼
