Martin Raum: Decomposition of an L2 space associated with a non-reductive group

Abstract:

Based on joint work with Jayadev Athreya, Jean Lagacé, and Martin Möller. The decomposition of square integrable functions on homogeneous spaces associated with reductive Lie groups is studied intensively in the Langlands program. Knowledge about this decomposition and in particular the connected spectral properties yields for example dynamic insight on orbit correlations. However, there are few examples of non-reductive Lie groups in the literature. I will present spectral and representation theoretic decompositions for the special affine group in two dimensions from three perspectives. Several features and in particular the multiplicities of the continuous spectrum contrast the case of reductive Lie groups.