Time: 9h00, Friday, December 5, 2014

Location: Room 109, Building A5, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi

Abstract:  The Langlands type discrete subgroups in real reductive groups can be non-arithmetic but, they admit also good properties for a spectral decomposition the discrete part $L^2_{disc}(\Gamma\backslash G)$ of $L^2(\Gamma\backslash G)$. The problem is reduced to computation of trace formula of discrete series representations, which are cohomologically induced.

We prove in this paper the trace formula for the discrete series cohomologically induced representations of real reductive groups with respect to Langlands type discrete subgroups. The traces are reduced to a combination of the Weyl trace formula and the Lefschetz' fixed point formula.

For the concrete examples SL(2,R), SL(3,R), SU(2,1), Sp(4,R) the formula were treated in papers Arxiv:1406.3018 math.RT, Arxiv:1407.6912 math.QA, Arxiv:1407.6909 math.RT, Arxiv:1407.6813 math.QA