Related papers: Induction automorphe pour les repr\'esentations el…

We characterize those regular, holomorphic or formal maps into the orbit space $V/G$ of a complex representation of a finite group $G$ which admit a regular, holomorphic or formal lift to the representation space $V$. In particular, the…

We characterize the extendibility of the normal curvature on frontals and we give a representation formula of this type of frontals. Also we give representation formulas for wavefronts on all types of singularities and others sub classes of…

An inductive realization of Loop Vertex Expansion is proposed and is applied to the construction of the $\phi_1^4$ theory. It appears simpler and more natural than the standard one at least for some situations.

We introduce a new integral representation for the standard L-function of an irreducible cuspidal automorphic representation of the exceptional group G2, and also for the twist of this L-function by an arbitrary character. Because our…

There are many Rankin-Selberg integrals representing Langlands $L$-functions, and it is not apparent what the limits of the Rankin-Selberg method are. The Dimension Equation is an equality satisfied by many such integrals that suggests a…

This paper presents the basic ideas and properties of elliptic functions and elliptic integrals as an expository essay. It explores some of their numerous consequences and includes applications to some problems such as the simple pendulum,…

We present a special class of examples of automorphic lifts of multiple tensor products of automorphic representations, motivated by combinatorial identities for Schur polynomials and a celebrated result of Newton and Thorne.

Let $\mathfrak g_i$ be a simple complex Lie algebra, $1\leq i \leq d$, and let $G=G_1\times...\times G_d$ be the corresponding adjoint group. Consider the $G$-module $V=\oplus r_i\mathfrak g_i$ where $r_i\geq 1$ for all $i$. We say that $V$…

Let $0 \to A \to L \to B \to 0$ be a short exact sequence of Lie algebras over a field $F$, where $A$ is abelian. We show that the obstruction for a pair of automorphisms in $\Aut(A) \times \Aut(B)$ to be induced by an automorphism in…

Generic extensions of aperiodic probability space automorphisms are recurrent.

Let $E:y^2=(x-e_1)(x-e_2)(x-e_3)$ be a nonconstant elliptic curve over $\mathbb{Q}(t)$, where $e_j\in \mathbb{Z}[t]$. We describe a method for finding a specialization $t\mapsto t_0\in\mathbb{Q}$ such that the specialization homomorphism is…

This paper introduces Linguistic Style Improvisation, a theory and set of algorithms for improvisation of spoken utterances by artificial agents, with applications to interactive story and dialogue systems. We argue that linguistic style is…

In this work, we describe a self-replication-based mechanism for designing agents of increasing complexity. We demonstrate the validity of this approach by solving simple, standard evolutionary computation problems in simulation. In the…

We introduce the notions of topological entropy of a formal language and of a topological automaton. We show that the entropy function is surjective and bound the entropy of languages accepted by deterministic {\epsilon}-free push-down…

This paper proposes bimorphic recursion, which is restricted polymorphic recursion such that every recursive call in the body of a function definition has the same type. Bimorphic recursion allows us to assign two different types to a…

We construct an endoscopic decomposition for local L-packets associated to irreducible cuspidal Deligne-Lusztig representations. Moreover, the obtained decomposition is compatible with inner twistings.

Proof assistants, such as Isabelle/HOL, offer tools to facilitate inductive theorem proving. Isabelle experts know how to use these tools effectively; however, they did not have a systematic way to encode their expertise. To address this…

For a given finite index inclusion of conformal nets $\mathcal{B}\subset \mathcal{A}$ and a group $G < \mathrm{Aut}(\mathcal{A}, \mathcal{B})$, we consider the induction and the restriction procedures for $G$-twisted representations. We…

Let X be a smooth projective surface over a number field, and $f: X \to X$ an automorphism of positive topological entropy. In this paper, we construct a height function on X that behaves well relative to f and deduce some arithmetic…

We classify all finite groups that have lifting property of mod $p$ representations to mod $p^2$ representations for all prime $p$.