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Transcript
SYMMETRY BREAKING OPERATORS FOR REDUCTIVE PAIRS MICHAEL PEVZNER Understanding of intertwining operators arising in branching laws of innite-dimensional representations of reductive Lie groups is a subtle problem mixing Combinatorics, Geometry, complex and real Analysis. Sometimes it turn out that such symmetry breaking operators are realized by dierential operators on appropriate functional spaces. A fundamental example of this phenomenon is given by the celebrated Rankin-Cohen brackets. We explain the algebraic and geometric nature of these operators and present a general method for their eective construction. We will illustrate these ideas with some concrete examples. 1
