Related papers: The functorial source problem via dimension data

Let $F$ be a global field. Let $G$ and $H$ be two connected reductive group defined over $F$ endowed with an $F$-morphism $f: H\rightarrow G$ such that the induced morphism $H_{der}\rightarrow G_{der}$ on the derived groups is a central…

The geometric Langlands correspondence has been interpreted as the mirror symmetry of the Hitchin fibrations for two dual reductive groups. This mirror symmetry, in turn, reduces to T-duality on the generic Hitchin fibers, which are smooth…

Let H be a connected reductive group over an algebraically closed field of characteristic zero, and let G be an abstract group. In this note we show that every homomorphism from the Grothendieck semiring of H to that of G which maps…

As a consequence of his numerical local Langlands correspondence for $GL(n)$, Henniart deduced the following theorem: If $F$ is a nonarchimedean local field and if $\pi$ is an irreducible admissible representation of $GL(n,F)$, then, after…

We describe an evolving and conjectural extension of the Langlands program for a class of nonlinear covering groups of algebraic origin studied by Brylinski-Deligne. In particular, we describe the construction of an L-group extension of…

The topological fundamental group $\pi_{1}^{top}$ is a topological invariant that assigns to each space a quasi-topological group and is discrete on spaces which are well behaved locally. For a totally path-disconnected, Hausdorff, unbased…

We study unitary pseudonatural transformations (UPTs) between fibre functors Rep(G) -> Hilb, where G is a compact quantum group. For fibre functors F_1, F_2 we show that the category of UPTs F_1 -> F_2 and modifications is isomorphic to the…

The Ichino-Ikeda conjecture, and its generalization to unitary groups by N. Harris, has given explicit formulas for central critical values of a large class of Rankin-Selberg tensor products. Although the conjecture is not proved in full…

Let $G$ be a simple group over a global function field $K$, and let $\pi$ be a cuspidal automorphic representation of $G$. Suppose $K$ has two places $u$ and $v$ (satisfying a mild restriction on the residue field cardinality), at which the…

Let $G$ be a simple connected complex Lie group. The additive eigencone of $G$ is a polyhedral cone containing the set of solutions to the additive eigenvalue problem, a generalization of the Hermitian eigenvalue problem. The additive…

In this paper we introduce a new algebraic device, which enables us to treat the quaternions as though they were a commutative field. This is of interest both for its own sake, and because it can be applied to develop an "algebraic…

Assume that $K$ is an algebraically closed field, $R$ a locally bounded $K$-category, $G$ an admissible group of $K$-linear automorphisms of $R$ and $F:R\rightarrow A$ the Galois $G$-covering functor. In the first part of the paper we show…

A functorial semi-norm on singular homology is a collection of semi-norms on the singular homology groups of spaces such that continuous maps between spaces induce norm-decreasing maps in homology. Functorial semi-norms can be used to give…

In this paper, we study a shrinking target problem with target at infinity in a homogeneous space of a semisimple algebraic group from the representation-theoretic point of view. Let $\rho:\mathbf G\to\mathbf{GL}(V)$ be an irreducible…

For a local field $F$ and an Artinian local coefficient ring $\Lambda$ with the same positive residue characteristic $p$ we define, for any $e\in{\mathbb N}$, a category ${\mathfrak C}^{(e)}(\Lambda)$ of ${\rm GL}_2(F)$-equivariant…

Let $\Pi$ be the fundamental group of a smooth variety X over $F_p$. Given a non-Archimedean place $\lambda$ of the field of algebraic numbers which is prime to p, consider the $\lambda$-adic pro-semisimple completion of $\Pi$ as an object…

It is a deep fact that the homotopy classification of topological manifolds is convariantly functorial. In other words, a map from a topological manifold M to another N naturally induces a map from the structure set S(M) to S(N). We extend…

Let $G$ be a complex connected reductive algebraic group and let $G_{\mathbb{R}}$ be a real form of $G$. We construct a sequence of functors $L_i\mathcal{R}$ from admissible (resp. finite-length) representations of $G$ to admissible (resp.…

We generalize the notion of semi-universality in the classical deformation problems to the context of derived deformation theories. A criterion for a formal moduli problem to be semi-prorepresentable is produced. This can be seen as an…

Unstable operations in a generalized cohomology theory E give rise to a functor from the category of algebras over E to itself which is a colimit of representable functors and a comonoid with respect to composition of such functors. In this…