#
Automorphic forms and harmonic analysis on covering groups

June 10 to June 14, 2013
at the

American Institute of Mathematics,
San Jose, California

organized by

Jeffrey Adams,
Wee Teck Gan,
and Gordan Savin

## Original Announcement

This workshop will be devoted to discussing extensions of the
the Langlands program to nonlinear groups in some generality. An
important example of such group is the metaplectic group: the
two-fold cover the symplectic group over a local field.
The focus of the workshop will be on foundational questions in the
harmonic analysis and the theory of automorphic forms on such groups.

The main topics for the workshop are:

- basic results in harmonic analysis and a theory of endoscopy for
nonlinear groups;
- formulation of a local Langlands correspondence for nonlinear groups;
- a theory of types for nonlinear groups;
- the trace formula and the structure of automorphic discrete spectrum.

While there have been many attempts to extend the Langlands philosophy
to covering groups in the past, these were largely confined to
specific families of examples.
In the past year, there have been a number of encouraging developments
regarding a general treatment. These developments strongly suggest
that a workshop devoted to the above foundational issues will be
especially timely. This workshop will gather the experts working on
different aspects of the problem, in order to take stock of and
consolidate these early progresses and to formulate the key questions
to be addressed in the immediate future.

## Material from the workshop

A list of participants.
The workshop schedule.

A report on the workshop activities.

A list of open problems.

Papers arising from the workshop:

The Langalands quotient theorem for finite central extensions of p-adic groups II: intertwining operators an duality

by Dubravka Ban and Chris Jantzen,

*Glas. Mat. Ser. III 51(71) (2016), no. 1, 153-163 * MR3516189The Langlands-Weissman Program for Brylinski-Deligne extensions

by Wee Teck Gan and Fan Gao

The Gindikin-Karpelevich Formula and Constant Terms of Eisenstein Series for Brylinski-Deligne Extensions

by Fan Gao

The conjectural relation between generalized Shalika models on SO4n(F) and the symplectic linear model on Sp4n(F). A Toy Example

by Agn`es David, Marcela Hanzer and Judith Ludwig,

*Women in numbers Europe, 87–107, Assoc. Women Math. Ser., 2, Springer, Cham, 2015 * MR3596602