Intertwining operators are ubiquitous in representation theory. Their construction typically requires a considerable amount of analysis, and they often assume an interesting form. For instance, they are frequently pseudodifferential operators associated with pseudodifferential calculi of intense current study in noncommutative geometry. Conversely, in all multiplicity-one decompositions of representations (e.g. the theta correspondence), the essentially unique intertwining operator, or its symbol, should encode important information on the representation-theoretic decomposition.

However, those operators have received little attention from within operator algebra theory. This meeting will be the occasion to present classical and recent aspects of the theory of intertwining operators and explore the connections between operator algebras and representation theory.

Topics of special interest will include:

• Symmetry breaking operators: special families of intertwining operators between representations of a group and a subgroup. These operators, for Lie groups and algebraic groups over local fields, are the subject of intense study in various settings via analytic, algebraic and geometric methods.

• Concrete study of the intertwining operators appearing in the theta-correspondence over local fields, including interpretations coming from operator algebras and noncommutative geometry.

• Applications of intertwining operators in equivariant index theory and noncommutative geometry, such as K-theoretic constructions based on the BGG complex.