Speaker: Jasmin Matz (Hebrew University)
Title: Effective limit multiplicities in SL(2,R^r \times C^s)
Abstract: For a lattice L in a semisimple Lie group G one can define a natural measure m_L on the unitary dual G^ of G which counts the multiplicities with which representations appears in the discrete part of L^2(L\G). When L varies over a family of lattices with vol(L\G) going to infinity, one expects in most cases m_L to tend to the Plancherel measure on G^. This has been proven to be true in many situations in which the lattices are either commensurable with each other, uniform in G, or G=SL(2,R), SL(2,C). In my talk I want to discuss this problem for the natural family of non-commensurable lattices L=SL(2,O_F) in G=SL(2,F \otimes R) when F runs over number fields with a fixed archimedean signature (r,s) and O_F is the ring of integers in F. In this case we also obtain a bound on the rate of convergence.