A Program for Branching Problems in the Representation Theory of Real Reductive Groups: Classification Problem of Symmetry Breaking Operators. Representation Theory inspired by the Langlands Conjectures (organized by B. Speh and P. Trapa), in connection with the AMS-AWM Noether lecture by Birgit Speh. Denver, USA, 17 January 2020.

A symmetry breaking operator is an intertwining operator that arises from branching problems of representations, thatis, an $H$-intertwining operator from an (irreducible) representation of $G$ to that of the subgroup $H$. It may be an integraloperator, and may be a more singular one such as a differential operator, when representations are realized geometrically. In general, it is a hard problem to classify symmetry breaking operators.

We plan to discuss a criterion for the spaceof symmetry breaking operators to be finite-dimensional, and a classification scheme of symmetry breaking operatorswith some examples for orthogonal groups.


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© Toshiyuki Kobayashi