Related papers: Smooth representations of GL(m,D), V: Endo-classes

Let G be a reductive p-adic group. We study how a local Langlands correspondence for irreducible tempered G-representations can be extended to a local Langlands correspondence for all irreducible smooth representations of G. We prove that,…

Let L be a finite extension of Qp, and let K be a spherically complete non-archimedean extension field of L. In this paper we introduce a restricted category of continuous representations of locally L-analytic groups G in locally convex…

In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…

We prove an analogue of Jacquet's conjecture on the local converse theorem for \ell-adic families of co-Whittaker representations of GL_n(F), where F is a finite extension of Q_p and \ell does not equal p. We also prove an analogue of…

Let G be any connected reductive group over a non-archimedean local field. We analyse the unipotent representations of G, in particular in the cases where G is ramified. We establish a local Langlands correspondence for this class of…

We compute the characters of simple supercuspidal representations of twisted GL(2n) and standard SO(2n+1) over a p-adic field. Comparing them by the endoscopic character relation, we determine the liftings of simple supercuspidal…

Let $D$ denote a quaternion division algebra over a non-archimedean local field $F$ with characteristic zero. Let $Sp_n(D)$ be the unique non-split inner form of the symplectic group $Sp_{2n}(F)$. An irreducible admissible representation…

The main result of this paper is a generalization of the theorem of Chevalley-Shephard-Todd to the rings of invariants of pseudo-reflection groups over regular domains. More precisely, let $A$ be a regular domain and let $K$ be its field of…

We consider the stratification of the category of smooth representations of $\mbox{GL}_n(F)$ (for $F$ a $p$-adic field) induced by degenerate Whittaker models. We show that, remarkably, the successive quotient categories in this…

We extend the calculus of relations to embed a regular category A into a family of pseudo-abelian tensor categories T(A,d) depending on a degree function d. Under the condition that all objects of A have only finitely many subobjects, our…

We provide an explicit construction of representations in the discrete spectrum of two $p$-adic symmetric spaces. We consider $\mathbf{GL}_n(F) \times \mathbf{GL}_n(F) \backslash \mathbf{GL}_{2n}(F)$ and $\mathbf{GL}_n(F) \backslash…

We study character varieties arising as moduli of representations of an orientable surface group into a reductive group $G$. We first show that if $G/Z$ acts freely on the representation variety, then both the representation variety and the…

Ces notes en fran\c{c}ais sont un r\'esum\'e de la pr\'epublication arXiv:1402.2501, o\`u en collaboration avec Peter Schneider, nous \'etablissons des formules de caract\`ere pour la s\'erie discr\`ete de GL(N) d'un corps local non…

The general linear group GL(n, K) over a field K contains a particularly prominent subgroup U(n, K), consisting of all the upper triangular unipotent elements. In this paper we are interested in the case when K is the finite field F_q, and…

We give a complete classification of simple representations of the braid group B_3 with dimension $\leq 5$ over any algebraically closed f ield. In particular, we prove that a simple d-dimensional representation $\rho: B_3 \to GL(V)$ is…

We study the geometry and cohomology of the (generic fibres) of formal deformation schemes of one-dimensional formal modules of finite height. By the work of Boyer (in mixed characterististic) and Harris and Taylor, the l-adic etale…

Given a quasi-split reductive group $G$ and a symmetric variety $X$, we introduce a notion of endoscopic varieties for $(G,X)$, and establish the foundational properties of these varieties such as matching of stable semi-simple orbits. To…

Let F be a global field and A its ring of adeles. Let G:=SL(2). We study the bilinear form B on the space of K-finite smooth compactly supported functions on G(A )/G(F) defined by the formula B (f,g):=B'(f,g)-(M^{-1}CT (f),CT (g)), where B'…

Let $F\subseteq H\subseteq G$ be closed subgroups of a locally compact group. In response to a 1972 question by Eymard, we construct an example where the homogeneous factor-space $G/F$ is amenable in the sense of Eymard-Greenleaf, while…

We describe an interesting interplay between symbolic dynamics, the structure of the Mandelbrot set, permutations of periodic points achieved by analytic continuation, and Galois groups of certain polynomials. Internal addresses are a…