We show that some types for supercuspidal representations of tamely ramified p-adic groups appear in Jiu-Kang Yu’s work are geometrizable. To do so, we define a function-sheaf dictionary one-dimensional characters arbitrary smooth group schemes over finite fields. In previous considered the case commutative and found standard definition character sheaves produced with nontrivial kernel. this pa...

For any unitary cuspidal representations πn of GLn(QA), n = 2, 3, 4, respectively, consider two automorphic representations Π and Π of GL6(QA), where Πp ∼= ∧π4,p for p 6= 2, 3 and π4,p not supercuspidal, and Π = π2 π3. First, Hypothesis H for Π and Π is proved. Then contributions from prime powers are removed from the prime number theorem for cuspidal representations π and π of GLm(QA) and GLm′...

We prove several multiplicity one theorems in this paper. For k a local field not of characteristic two, and V a symplectic space over k, any irreducible admissible representation of the symplectic similitude group GSp(V ) decomposes with multiplicity one when restricted to the symplectic group Sp(V ). We prove the analogous result for GO(V ) and O(V ), where V is an orthogonal space over k. Wh...

We exhibit a basis for the space of spherical characters of a distinguished supercuspidal representation π of a connected reductive p-adic group, subject to the assumption that π is obtained via induction from a representation of an open compact mod centre subgroup. We derive an integral formula for each spherical character belonging to the the basis. This formula involves integration of a part...