Representation Theory & Noncommutative Geometry

The purpose of this seminar is to present recent developments in the representation theory of real reductive groups and related areas.
The time slots were chosen so that researchers from both Asia and Europe can attend.
We hope that this meeting also helps to bring together Asian and European colleagues within the AIM Research Community Representation Theory & Noncommutative Geometry.

**Abstracts**

T. Kobayashi |
Tempered representations and limit algebras | Slides |

C.-B. Zhu |
Theta correspondence and special unipotent representations | Slides |

W. T. Gan |
Twisted GGP problems and conjectures | Slides |

B. Sun |
Archimedean period relations and period relations for automorphic L-functions | Slides |

Y. Oshima |
On the asymptotic support of Plancherel measures for homogeneous spaces | Slides |

In Representation Theory, branching problems ask how a given irreducible representation $\pi$ of a group $G$ behaves when restricted to subgroups $G'\subset G$.
The decomposition of the tensor product of two irreducible representations (fusion rule) is a special case of this problem, where $(G,G')$ is of the form $(G_1 \times G_1, \Delta(G_1))$.
In the general setting where $(G,G')$ is a pair of reductive groups and $\pi$ is an infinite dimensional representation of $G$,
branching problems include various important situations such as theta correspondence and the Grossâ€“Prasadâ€“Gan conjecture, and branching laws may involve "wild behaviors"
such as infinite multiplicities and continuous spectrum.

This workshop is devoted to recent progress in this area, with a particular emphasis on new analytical methods.

**Abstracts**

T. Kubo |
Differential symmetry breaking operators for $(O(n+1,1),O(n,1))$ on differential forms | Slides |

R. Nakahama |
Computation of weighted Bergman inner products on bounded symmetric domains for $SU(r,r)$ and restriction to subgroups | Slides |

Q. Labriet |
Symmetry breaking operators and orthogonal polynomials | Slides |

Toward a holographic transform for the quantum Clebsch-Gordan formula | Slides |