相关论文: Unicity of types and local Jacquet--Langlands corr…

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 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 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 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…

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, $A$ be a central simple $F$-algebra, and $G$ be the multiplicative group of $A$. It is known that for every irreducible supercuspidal representation $\pi$, there exists a $[G, \pi]_{G}$-type $(J,…

Let $F$ be a non-Archimedean local field, with the ring of integers $\mathfrak{o}_F. Let $G=GL_N(F)$, $K=GL_N(\mathfrak{o}_F)$ and $\pi$ a supercuspidal representation of $G$. We show that there exist a unique irreducible smooth…

Let $F$ be a locally compact non-Archimedean field, and let $B/F$ be a division algebra of dimension 4. The Jacquet-Langlands correspondence provides a bijection between smooth irreducible representations of $B^\times$ of dimension $>1$ and…

We establish the unicity of types for depth-zero supercuspidal representations of an arbitrary $p$-adic group $G$, showing that each depth-zero supercuspidal representation of $G$ contains a unique conjugacy class of typical representations…

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 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…

Let G be a general linear group over a p-adic field and let D^* be an anisotropic inner form of G. The Jacquet-Langlands correspondence between irreducible complex representations of D^* and discrete series of G does not behave well with…

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…

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…

We prove a full global Jacquet-Langlands correspondence between GL(n) and division algebras over global fields of non zero characteristic. If $D$ is a central division algebra of dimension $n^2$ over a global field $F$ of non zero…

We propose a generalisation of the Jacquet-Langlands correspondence to the whole Grothendieck group of finite lenght admissible representations. As an application we prove some particular cases of the global Jacquet-Langlands…

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…

The classical McKay correspondence for finite subgroups $G$ of $\SL(2,\C)$ gives a bijection between isomorphism classes of nontrivial irreducible representations of $G$ and irreducible components of the exceptional divisor in the minimal…

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…

Let $F$ be a non-Archimedean local field with odd characteristic $p$. Let $N$ be a positive integer and $G=Sp_{2N}(F)$. By work of Lomel\'i on $\gamma$-factors of pairs and converse theorems, a generic supercuspidal representation $\pi$ of…