Generalizing theta correspondences
July 28 to August 1, 2008
American Institute of Mathematics,
Palo Alto, California
Wee Teck Gan and Gordan Savin
This workshop concerns extensions
and applications of the method of theta correspondence, including a
discussion of outstanding problems and future directions.
Specific topics include
- Exceptional theta correspondence. The setting of theta correspondence
was extended from the classical setting of metaplectic groups to the case of
other groups, most notably the exceptional groups.
- Restriction of small representations of classical groups. Some recent work of Ginzburg
and Ikeda uses small representations
to construct examples of CAP representations.
- Small representations of covering groups. In a recent work of
Bump-Friedberg-Ginzburg and Loke-Savin, small representations of covering groups of
orthogonal groups are constructed and then exploited to produce examples of liftings
- Backward lifting. This is a method pioneered by Ginzburg-Rallis-Soudry to
construct the backward lifting from $GL(n)$ to classical groups.
- Arithmetic applications. These include special values, non-vanishing and location
of zeros of L-functions, applications to p-adic L-functions as well as period
integrals and Gross-Prasad conjecture.
Material from the workshop
A list of participants.
The workshop schedule.
A report on the workshop activities.