Symmetry Breaking Operators: General Theory and Concrete Construction for Reductive Groups (opening lecture/2 lectures). Representation Theory of Lie Groups, Mathematical Physics, and Dynamical Systems. Université de Reims, France, 24-29 June 2019.

The lectures highlight infinite-dimensional representations of real reductive groups with focus on induction and restriction. I begin with the general results such as geometric criterion for finiteness (of uniform boundedness) of the multiplicities of irreducible representations occurring in induction and restriction.

Symmetry breaking operators are morphisms that describe restriction of representations. In the second lecture, I plan to discuss construction problem of ''symmetry breaking operators in a concrete geometric setting.

[ program (pdf) ]

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© Toshiyuki Kobayashi