Dimension formulae of Gelfand-Graev, Jones and their relation to automorphic forms and temperdness of quasiregular representations

02.06.2022 12:00 - 12:50

Florin Radulescu (IMAR and Rome)

Vaughan Jones introduced a formula computing the von Neumann dimension for the restriction to a lattice of the left regular representation of a semisimple Lie group.

It is a variant of a formula by Atiah Schmidt computing  the formal  dimension in the Haris Chandra trace formula for discrete series. It is surprisingly similar (in the case of PSL(2,Z)) to the dimension of the space of automorphic forms and is similar to a formula proved by Gelfand, Graev.  We use an extension of this formula to provide a method for computing the formal trace of representations of PSL(2,Q_p) (or more general situations), when analyzing the quasi regular representation on PSL(2,R)/PSL(2,Z). It provides a method to obtain estimates for eigenvalues of  Hecke operators.

This will be a hybrid seminar. The live speaker in SR10 will also be streamed on Zoom.

Join Zoom meeting ID 
613 8691 2732 or via the link below.

Organiser:

G. Arzhantseva, Ch. Cashen, Y. Lodha

Location:

SR 10, 2. OG., OMP 1