Unitary representations, automorphic and modular forms
Grant no. 3628 supported by Croatian Science Foundation
In project Unitary representations, automorphic and modular forms we are joining a new wave of research in the framework of Langlands program which stems from the recent results of Arthur and collaborators. We explore two intertwining themes: unitary representations of reductive p-adic (and related) groups and classical modular and automorphic forms. In the research of the unitary dual of classical groups, using, among other things, Moeglin’s results about construction of A-packets, we intend to construct large families of unitary representations. We plan to do that by analysing parabolically induced representations of a special type and determine the composition series. By doing this, we generalize many results of Speh, Tadić, Muić, Matić and Hanzer. We intend to analyse automorphic representations of global classical groups primarily using Eisenstein series, in a way that was previously used in the works of Muić and Hanzer, and some recent results of Arthur about endoscopy. From these results, we intend to get information about L-functions, and in getting those knowledge, we intend to use results obtained in our research in local theory. On the other hand, the results on the Eisenstein series can be applied on the classical modular forms. We also intend to obtain new modular forms and analyse them using Poincare series, examining non-vanishing conditions and thus generalizing previous work of Muić. Also we want to find explicit bases for the spaces of modular forms. In the research of the representations of metaplectic group, we mostly intend to focus on generic representations, and we intend to use recent results of Savin, Takeda, Lapid, Atobe and Gan about construction of local factors and theta correspondence.