Related papers: The Local Jacquet-Langlands Correspondence Via Fou…

Let $F$ be a non-Archimedean locally compact field of residual characteristic $p$ with $p\neq 2$. Let $n$ be a power of $p$ and let $G$ be an inner form of the general linear group $\text{\rm GL}_n(F)$. We give a transparent parametrization…

In this paper, we give a purely geometric approach to the local Jacquet-Langlands correspondence for GL(n) over a p-adic field, under the assumption that the invariant of the division algebra is 1/n. We use the l-adic etale cohomology of…

Let F be a non-Archimedean local field and let E be an unramified extension of F of degree n>1. To each sufficiently generic multiplicative character of E (the details are explained in the body of the paper) one can associate an irreducible…

Let F be a non-archimedean local field of characteristic zero with residual characteristic p. In this paper, we present a simple proof and construction of the local Langlands correspondence for simple supercuspidal representations of…

We prove that the global Jacquet--Langlands correspondence ${\rm JL}$ for ${\rm GL}(2)$ can be realized via tensor products over Hecke algebras. Let $G$ be a non-split inner form of ${\rm GL}(2)$ over a number field. Using the similitude…

Let E/F be a quadratic extension of p-adic fields. The local Langlands correspondence establishes a bijection between n-dimensional Frobenius semisimple representations of the Weil-Deligne group of E and smooth, irreducible representations…

In this paper we show a local Jacquet-Langlands correspondence for all unitary irreducible representations. We prove the global Jacquet-Langlands correspondence in characteristic zero. As consequences we obtain the multiplicity one and…

Let $F$ be a non-Archimedean local field of residual characteristic $p$, and $\ell$ a prime number, $\ell \neq p$. We consider the Langlands correspondence, between irreducible, $n$-dimensional, smooth representations of the Weil group of…

For $E/F$ quadratic extension of local fields and $G$ a reductive algebraic group over $F$, the paper formulates a conjecture classifying irreducible admissible representations of $G(E)$ which carry a $G(F)$ invariant linear form, and the…

Let G be a connected reductive group over a non-archimedean local field K, and assume that G splits over an unramified extension of K. We establish a local Langlands correspondence for irreducible unipotent representations of G. It comes as…

Let $F$ be a non-archimedean local field. For any irreducible representation $\pi$ of an inner form $G'=\mathrm{GL}_{m}(D)$ of $G=\mathrm{GL}_{N}(F)$, there exists an irredubile representation of a maximal compact open subgroup in $G'$…

We show how the modular representation theory of inner forms of general linear groups over a non-Archimedean local field can be brought to bear on the complex theory in a remarkable way. Let F be a non-Archimedean locally compact field of…

Let K/F be a tamely ramified quadratic extension of non-archimedean locally compact fields. Let GL_m (D) be an inner form of GL_n (F) and GLp(R) = (M_m (D) \otimes K)^{\times} . Then GLp(R) is an inner form of GL_n (K). In this work, we…

We give a description of the local Jacquet-Langlands correspondence for simple supercuspidal representations via type theory. As a consequence, we show that the endo-classes for such representations are invariant under the local…

Let F be a non-archimedean local field. We establish the local Langlands correspondence for all inner forms of the group $SL_n (F)$. It takes the form of a bijection between, on the one hand, conjugacy classes of Langlands parameters for…

Let $F$ be a non-Archimedean local field with residue field $k$ of odd characteristic, and let $B/F$ be the division algebra of rank 4. We explicitly construct a stable curve $\mathfrak{X}$ over the algebraic closure of $k$ admitting an…

Let K/F be a quadratic extension of non archimedean local fields. Let V be an irreducible level zero discrete series representation of the group G = GL2(R), where R is a division algebra of center K and of index r. One assumes that V is not…

Let F be a p-adic field and n a positive integer. The local Langlands conjecture asserts the existence of a bijection between irreducible admissible representations of GL(n,F) and n-dimensional admissible representations of the Weil-Deligne…

Let F be a non-Archimedean local field of residual characteristic p, and {\ell} be a prime number different from p. We consider the local Jacquet-Langlands correspondence between {\ell}-adic discrete series of GL(n,F) and an inner form…

We determine the parity of the Langlands parameter of a conjugate self-dual supercuspidal representation of GL(n) over a non-archimedean local field by means of the local Jacquet-Langlands correspondence. It gives a partial generalization…