2011/03/31 by Lior Silberman, Silberman, Lior
Mathematics · #22E50 #43A85 #FOS: Mathematics #Geometry and complex manifolds #Mathematical Dynamics and Fractals #Representation Theory (math.RT) #advanced mathematical theories #math.RT #msc:22E50 #msc:43A85
paper · pdf · doi:10.48550/arxiv.1104.0074
15 pages
openalex publication_date 2011/03/31 · arxiv created 2011/04/01 · arxiv updated 2011/04/04 · openalex created_date 2022/09/27 · openalex updated_date 2026/07/28
Given a measure μ on a locally symmetric space Y=Γ\backslash G/K, obtained as a weak-* limit of probability measures associated to eigenfunctions of the ring of invariant differential operators, we construct a measure μ on the homogeneous space X=Γ\backslash G which lifts μ and which is invariant by a connected subgroup A1⊂ A of positive dimension, where G=NAK is an Iwasawa decomposition. If the functions are, in addition, eigenfunctions of the Hecke operators, then μ is also the limit of measures associated to Hecke eigenfunctions on X. This generalizes previous results of the author and A. Venkatesh to the case of "degenerate" limiting spectral parameters.