Intertwining operators and geometry

Representation Theory and Noncommutative Geometry

Workshop: Intertwining operators and geometry

January 20 to 24, 2025 - IHP, Paris

Summary

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.

Preliminary list of speakers:

• Corina Ciobotaru
• Pierre Clare
• Toshiyuki Kobayashi
• Hung Yean Loke
• Bent Orsted
• Bram Mesland
• Tomasz Przebinda
• Birgit Speh
• Michael Pevzner
• Hang Wang

Organising Committee:

• Jan Frahm
• Angela Pasquale

Scientific Committee:

• Monica Nevins
• Michael Pevzner
• Birgit Speh
• Robert Yuncken

Contributed talks:

We are opening proposals for a few short talks during the workshop. These talks will be aimed at early-career researchers and will last 30 to 40 minutes. We invite interested colleagues to fill out this form: 

Short talk application form