Related papers: Affine Springer fibers and depth zero L-packets

The goal of this work is to construct a perverse t-structure on the infinity-category of l-adic LG-equivariant sheaves on the loop Lie algebra Lg and to show that the affine Grothendieck-Springer sheaf S is perverse. Moreover, S is an…

We define a new cohomology set for an affine algebraic group G and a multiplicative finite central subgroup Z, both defined over a local field of characteristic zero, which is an enlargement of the usual first Galois cohomology set of G. We…

We consider the approximate properties of tight wavelet frames on Vilenkin group $G$. Let $\{G_n\}_{n\in \mathbb{Z} }$ be a main chain of subgroups, $X$ be a set of characters. We define a step function $\lambda({\chi})$ that is constant on…

We generalize the work of DeBacker and Reeder to the case of unitary groups split by a tame extension. The approach is broadly similar and the restrictions on the parameter the same, but many of the details of the arguments differ. Let $G$…

Consider a standard representation $\pi_{st}$ of a quasi-split reductive p-adic group G. The generalized injectivity conjecture, posed by Casselman and Shahidi, asserts that any generic irreducible subquotient $\pi$ of $\pi_{st}$ is…

Let F be a non-Archimedean locally compact field with residual characteristic p, let G be an inner form of GL(n,F) for a positive integer n and let R be an algebraically closed field of characteristic different from p. When R has…

This is an expanded version of the text ``Perverse Sheaves on Loop Grassmannians and Langlands Duality'', AG/9703010. The main new result is a topological realization of algebraic representations of reductive groups over arbitrary rings. We…

Let $R$ be the ring of integers in a finite extension $K$ of $\mathbb{Q}_p$, let $k$ be its residue field and let $\chi:\pi_1(X)\to R^{\times}=GL_{1}(R)$ be a "geometric" rank one representation of the arithmetic fundamental group of a…

Let $(\pi, \mathcal H)$ be a continuous unitary representation of the (infinite dimensional) Lie group $G$ and $\gamma \: \mathbb R \to \mathrm{Aut}(G)$ define a continuous action of $\mathbb R$ on $G$. Suppose that $\pi^\#(g,t) = \pi(g)…

This work is the geometric part of our proof of the weighted fundamental lemma, which is an extension of Ng\^o Bao Ch\^au's proof of the Langlands-Shelstad fundamental lemma. Ng\^o's approach is based on a study of the elliptic part of the…

Let $F$ be a non-archimedean locally compact field. We study a class of Langlands-Shahidi pairs $({\bf H},{\bf L})$, consisting of a quasi-split connected reductive group $\bf H$ over $F$ and a Levi subgroup $\bf L$ which is closely related…

An $F$-zip over a scheme $S$ over a finite field is a certain object of semi-linear algebra consisting of a locally free module with a descending filtration and an ascending filtration and a $\Frob_q$-twisted isomorphism between the…

Let $F$ be a $p$-adic field with residue field of cardinality $q$. To each irreducible representation of $GL(n,F)$, we attach a local Euler factor $L^{BF}(q^{-s},q^{-t},\pi)$ via the Rankin-Selberg method, and show that it is equal to the…

Let $A$ be a simple abelian variety of dimension $g$ defined over a finite field $\mathbb{F}_q$ with Frobenius endomorphism $\pi$. This paper describes the structure of the group of rational points $A(\mathbb{F}_{q^n})$, for all $n \geq 1$,…

Let F be a locally compact non-archimedean field and G the group of F-rational points of an algebraic group assumed to be defined over F, semisimple, simply connected and of F-rank 1. Let pi be a complex irreducible supercuspidal…

Let $G$ be a reductive group over a non-archimedean local field $F$ of residue characteristic $p$. We consider pairs $(\phi,I)$ consisting of a "wild inertia" Langlands parameter $\phi: P_F \longrightarrow \hat{G}$ whose centralizer…

Each signature $\underline{\lambda}(n)=(\lambda_1(n),\dots,\lambda_n(n))$, where $\lambda_1(n)\geq\dots\geq\lambda_n(n)$ are integers, gives an irreducible representation…

Let $F$ be a non-archimedean local field, of characteristic 0. Let $V$ be a finite dimensional vector space over $F$ and $q$ be a non-degenerate quadratic form on $V$. Denote $G$ the special orthogonal group of $(V,q)$. Let $W$ a…

For a quasi-split connected reductive group $G$ over a local field $F$ we define a compact abelian group $\tilde\pi_1(G)$ and an extension $1 \to \tilde\pi_1(G) \to G(F)_\infty \to G(F) \to 1$ of topological groups equipped with a splitting…

Let $G$ be a group with subgroup $H$, and let $(\pi,V)$ be a complex representation of $G$. The natural action of the normalizer $N$ of $H$ in $G$ on the space $\mathrm{Hom}_H(\pi,\mathbb{C})$ of $H$-invariant linear forms on $V$, provides…