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...

It is surprising that the following question has not been addressed in the literature: what is the contragredient in terms of Langlands parameters? Thus suppose G is a connected, reductive algebraic group defined over a local field F , and G(F ) is its F -points. According to the local Langlands conjecture, associated to a homomorphism φ from the Weil-Deligne group of F into the L-group of G(F ...

This paper considers the question of relative hyperbolicity of an Artin group with regard to the geometry of its associated Deligne complex. We prove that an Artin group is weakly hyperbolic relative to its finite (or spherical) type parabolic subgroups if and only if its Deligne complex is a Gromov hyperbolic space. For a 2-dimensional Artin group the Deligne complex is Gromov hyperbolic preci...

For example, suppose that G ∼= S9 and H ∼= S8, where Sn denotes the symmetric group on n letters. Then ρ is one of the two absolutely irreducible representations of G of dimension 8, and according to our theorem there exists an elliptic curve E over M such that ρ occurs in Q⊗E(K). The other absolutely irreducible representation of G of dimension 8 is ρ ⊗ , where is the “sign” character of G, an...

We prove a realization of the local Langlands correspondence for two-dimensional representations Weil group conductor three in cohomology Lubin–Tate curves by purely geometric method.