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

We construct integrable pseudopotentials with an arbitrary number of fields in terms of elliptic generalization of hypergeometric functions in several variables. These pseudopotentials yield some integrable (2+1)-dimensional hydrodynamic…

We obtain an algorithmic construction of the isotropy lattice for a lifted action of a Lie group $G$ on $TM$ and $T^*M$ based only on the knowledge of $G$ and its action on $M$. Some applications to symplectic geometry are also shown.

Automorphic loops are loops in which all inner mappings are automorphisms. A large class of automorphic loops is obtained as follows: Let $m$ be a positive even integer, $G$ an abelian group, and $\alpha$ an automorphism of $G$ that…

We introduce an orbifold induction procedure which provides a systematic construction of cyclic orbifolds, including their twisted sectors. The procedure gives counterparts in the orbifold theory of all the current-algebraic constructions…

The present work is devoted to the extension of some general properties of automorphisms and derivations which are known for Lie algebras to finite dimensional complex Leibniz algebras. The analogues of the Jordan-Chevalley decomposition…

Given a morphism of (small) groupoids with injective object map, we provide sufficient and necessary conditions under which the induction and co-induction functors between the categories of linear representations are naturally isomorphic. A…

The Jacobian elliptic functions are generalized and applied to a nonlinear eigenvalue problem with $p$-Laplacian. The eigenvalue and the corresponding eigenfunction are represented in terms of common parameters, and a complete description…

We show that on an Abelian variety over an algebraically closed field of positive characteristic, the obstruction to lifting an automorphism to an Abelian variety over a field of characteristic zero as a morphism vanishes if and only if it…

We give parameterizations of the irreducible representations of finite groups of Lie type in their defining characteristic.

We compare real and complex dynamics for automorphisms of rational surfaces that are obtained by lifting \chg{some} quadratic birational maps of the plane. In particular, we show how to exploit the existence of an invariant cubic curve to…

Abstraction is key to scaling up reinforcement learning (RL). However, autonomously learning abstract state and action representations to enable transfer and generalization remains a challenging open problem. This paper presents a novel…

Topological transforms have been very useful in statistical analysis of shapes or surfaces without restrictions that the shapes are diffeomorphic and requiring the estimation of correspondence maps. In this paper we introduce two…

Among (isotopy classes of) automorphisms of handlebodies those called irreducible (or generic) are the most interesting, analogues of pseudo-Anosov automorphisms of surfaces. We consider the problem of isotoping an irreducible automorphism…

Autoencoders are techniques for data representation learning based on artificial neural networks. Differently to other feature learning methods which may be focused on finding specific transformations of the feature space, they can be…

We define a new kind of automata recognizing properties of data words or data trees and prove that the automata capture all queries definable in Regular XPath. We show that the automata-theoretic approach may be applied to answer…

The automorphisms of all 4-dimensional, real Lie Algebras are presented in a comprehensive way. Their action on the space of $4\times 4$, real, symmetric and positive definite, matrices, defines equivalence classes which are used for the…

We develop a fully automatic image colorization system. Our approach leverages recent advances in deep networks, exploiting both low-level and semantic representations. As many scene elements naturally appear according to multimodal color…

Let $G$ be a split simply-connected group of type $D$ or $E$. The minimal automorphic representation $\Pi$ of $G(\mathbb A)$ admits a realization on a space of functions $\mathcal S(X(\mathbb A))$ for a variety $X$. In this paper we write…

This paper analyzes the correctness of the subsumption algorithm used in CLASSIC, a description logic-based knowledge representation system that is being used in practical applications. In order to deal efficiently with individuals in…

We prove that there exists an automorphism of C^2 tangent to the identity with a domain of attraction to the origin, biholomorphic to the origin, along a degenerate characteristic direction.