Appears in collection : 2025 - T1 - WS1 - Intertwining operators and geometry

For unitary representations of a reductive Lie group, in addition to finding all equivalence classes, there is the problem of describing concrete models of individual representations. This is important for several applications, note the example of the metaplectic representation for the double cover of the symplectic group. For the covering group of three by three real matrices of determinant one, there is an analogous representation studied by many authors, in particular P. Torasso who gave a concrete model. We shall describe other models using intertwining operators, both differential and integral operators. This talk is based on work with T. Kubo and a thesis by T. T. Dahl; also some open problems are stated for this representation.