We study the restriction of Zuckerman’s derived functor modules for symmetric pairs of real reductive groups assuming that it is discretely decomposable. We obtain explicit branching laws in this setting by case-by-case calculations based on the classification. We show that the restriction decomposes as a direct sum of Zuckerman’s derived functor modules for the subgroup. A key ingredient of the proof is the realization of representations as \(\mathcal {D}\) -modules on the flag variety.

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Discrete Branching Laws of Derived Functor Modules

  • Yoshiki Oshima

摘要

We study the restriction of Zuckerman’s derived functor modules for symmetric pairs of real reductive groups assuming that it is discretely decomposable. We obtain explicit branching laws in this setting by case-by-case calculations based on the classification. We show that the restriction decomposes as a direct sum of Zuckerman’s derived functor modules for the subgroup. A key ingredient of the proof is the realization of representations as \(\mathcal {D}\) -modules on the flag variety.