In our talk we will outline possible approach to the unitarizability problem in the case of classical p-adic groups and possible role which could play automorphic representations in it. Special attention will be devoted to the question what could be the isolated representations in the unitary duals of these groups. We will review known facts and discuss some conjectures.
Marko Tadić graduated mathematics in 1976 and got Ph.D. in 1980 at University of Zagreb. He has been full-professor there since 1987. In 2000, he became fellow of Croatian Academy of Sciences and Arts and also member of Academia Europea. Tadić works in representation theory of reductive p-adic groups and its connections with modern theory of automorphic forms. He classified irreducible unitary representations and got formula for their characters in the case of p-adic general linear groups. He described structure expliciting interaction of parabolic induction and Jacquet modules, he got explicit construction of discrete series for classical groups (jointly with C. Mœglin), and classified several classes of irreducible unitary representations of classical p-adic groups. These are some of his contributions: Tadić has been visiting and lecturing at number of universities and institutes including University of Chicago, Université Paris 7, Max-Planck-Institute für Mathematik (Bonn), University of Utah, Sonder- forschungsbereich 170, Geometrie und Analysis (Göttingen), Mathematisches Institut Der Universität Münster, The Hong Kong University of Science and Technology, Institute of Mathematical Sciences (Singapore), Weizmann Institute of Science (Rehovot), Erwin Schrödinger International Institute for Mathematical Physics (Vienna) etc.
