Kavli Affiliate: Toshiyuki Kobayashi
| First 5 Authors: Michael Harris, Michael Harris, , ,
| Summary:
We study properties of the restriction of discrete series representations of
$G=U(p,q)$ to $G’= U(p-1,q)$ and the corresponding symmetry breaking operators
in $operatornameHom_G'(pi|_G’, pi’)$. This leads to the introduction
of elementary and coherent pairs of discrete series representations and their
classification. Translations of symmetry breaking operators are defined via
tensor products with finite-dimensional representations, which leads to the
study of the coherent cohomology of discrete series representations under
restriction and translations. This is applied to the study of cup products of
coherent cohomology of associated Shimura varieties, and to the arithmetic of
central values of certain Rankin–Selberg $L$-functions of $GL(n+1)times
GL(n)$.
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