Restrictions of Representations of Classical Groups: Examples Wee Teck Gan, Benedict H. Gross and Dipendra Prasad

Symplectic Local Root Numbers, Central Critical L-values, and Restriction Problems in the Representation Theory of Classical Groups Wee Teck Gan, Benedict H. Gross and Dipendra Prasad

Fourier transform and the global Gan–Gross–Prasad conjecture for unitary groups

By the relative trace formula approach of Jacquet–Rallis, we prove the global Gan– Gross–Prasad conjecture for unitary groups under some local restrictions for the automorphic representations.

Fourier–jacobi Periods of Classical Saito–kurokawa Lifts

Kohnen–Skuroppa [8] proved a formula for the ratio of the Petersson inner products of the half integral weight modular form and its Saito–Kurokawa lifting. We give an interpretation of this formula in the frame work of the refined Gan–Gross–Prasad conjecture. This provides us with an example of the refined Gan–Gross–Prasad conjecture for the nontempered representations.

Distinguished Representations for Sl ( 2 )

Let E/F be a quadratic extension of p-adic fields. We compute the multiplicity of the space of SL2(F )-invariant linear forms on a representation of SL2(E). This multiplicity varies inside an L-packet similar in spirit to the multiplicity formula for automorphic representations due to Labesse and Langlands.

EXTENSIONS OF REPRESENTATIONS OF p-ADIC GROUPS

We calculate extensions between certain irreducible admissible representations of p-adic groups. To Hiroshi Saito, in memoriam