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 study a problem concerning parabolic induction in certain p-adic unitary groups. More precisely, for $E/F$ quadratic extension of fields the associated group $G=\mathrm{U}(n,n)$ contains subgroup $P$ with Levi component $L$ isomorphic to $\mathrm{GL}_n(E)$. Let $\pi$ be an irreducible supercuspidal representation depth zero. use Hecke algebra methods determine when parabolically induced $\io...