Workshop on Representation Theory and Analysis on Locally Symmetric Spaces | |

Topic: | The Plancherel formula for $L^2(GL_n(F)\backslash GL_n(E))$ and applications to the Ichino-Ikeda and formal degree conjectures for unitary groups |

Speaker: | Raphael Beuzart-Plessis |

Affiliation: | Centre national de la recherche scientifique |

Date: | Tuesday, March 6 |

Time/Room: | 11:30am - 12:30pm/Simonyi Hall 101 |

Video Link: | https://video.ias.edu/RepTheoryAnalysisLocallySymmetricSpaces/2018/0306-RaphaelBeuzart-Plessis |

Abstract : Let $E/F$ be a quadratic extension of local fields of characteristic zero. In this talk, I will explain two ways to compute the Plancherel decomposition of $L^2(GL_n(F)\backslash GL_n(E))$. In both cases, the result involves the image of base change from unitary groups to $GL_n(E)$ and is in accordance with a general conjecture of Sakellaridis-Venkatesh on the spectral decomposition of spherical varieties. We will also give applications of our formulas to the so-called Ichino-Ikeda and formal degree conjectures for unitary groups.