Afternoon Representation Theory 2 - Institut Élie Cartan de Lorraine

Date/heure
23 mars 2021
13:45 - 17:10

Lieu
Zoom

Catégorie d'évènement
Analyse et théorie des nombres

13:45 – 14:40: Alessandra IOZZI (ETH Zürich)

The real spectrum compactification of character varieties: characterizations and applications

We describe properties of a compactification of general character varieties with good topological properties and give various interpretations of its ideal points. We relate this to the Thurston-Parreau compactification and apply our
results to the theory of maximal representations.

This is a joint work with Marc Burger, Anne Parreau and Maria Beatrice Pozzetti.

15:00 – 15:55: Raphaël BEUZART-PLESSIS (Aix-Marseille Université and CNRS)

Multipliers and isolation of the cuspidal spectrum by convolution operators

Let $G$ be a real reductive algebraic group and $Γ$ ; be an arithmetic lattice of $G$ .
In this talk, I will explain how to generalize a construction of Lindenstrauss-Venkatesh giving rise to certain operators on $L^{2} (Γ ∖ G)$ with image in the cuspidal subspace. These operators can be written, in the adelic setting, as combinations of convolution operators at Archimedean places and $p$ -adic places (Hecke operators). A crucial ingredient of the proof is the existence of sufficiently many multipliers of $G$ acting on the space of smooth functions with rapid decay (but not necessarily $K$ -finite).
Time permitting, I will also describe one application of this construction to the global Gan-Gross-Prasad conjecture for unitary groups.
This talk is based on joint work with Yifeng Liu, Wei Zhang and Xinwen Zhu.

16:15 – 17:10: Erik VAN DEN BAN (University of Utrecht)

The Harish-Chandra transform for Whittaker functions

I will discuss the role of the descent transform in Harish-Chandra’s approach to the Plancherel formula for Whittaker functions, presented in the posthumous volume 5 of his collected works (Springer 2018). At an earlier occasion I explained how the proof of the Plancherel theorem can be completed by using a Paley-Wiener shift technique. In the present talk I will explain how the proof can be completed in a more straightforward way, by using a suitable result on wave packets of Whittaker functions.

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Contacts

To register as a participant or for further information, please contact one of the organizers: Salah Mehdi or Angela Pasquale.