Related papers: Motives and Automorphic Representations
Motivic homotopy theory is meant to play the role of algebraic topology, in particular homotopy theory, in the context of algebraic geometry. As proved by Oliver Rondigs and Paul Arne Ostvaer, this theory is closely connected to Voevodsky's…
In this paper, we study extra-twists for automorphic representations of $\mathrm{GL}_n$ and use them to give a precise description of the image of the Galois representations associated with regular algebraic cuspidal automorphic…
Representations over diagrams of abelian categories unify quite a few notions appearing widely in literature such as representations of categories, presheaves of modules over categories, representations of species, etc. In this series of…
We say that there is a representation of the universal algebra B in the universal algebra A if the set of endomorphisms of the universal algebra A has the structure of universal algebra B. Therefore, the role of representation of the…
Theory of representations of universal algebra is a natural development of the theory of universal algebra. In the book, I considered representation of universal algebra, diagram of representations and examples of representation. Morphism…
In 1967, Langlands conjectured a natural correspondence between automorphic representations and Galois representations, over number fields as well as over function fields. In 1983, Drinfeld discovered a geometric analog of the Langlands…
The geometric Langlands correspondence for complex algebraic curves differs from the original Langlands correspondence for number fields in that it is formulated in terms of sheaves rather than functions (in the intermediate case of curves…
The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to…
Geometric symmetry induces symmetries of function spaces, and the latter yields a clue to global analysis via representation theory. In this note we summarize recent developments on the general theory about how geometric conditions affect…
We survey some recent developments at the interface of algebraic geometry, surface topology, and the theory of ordinary differential equations. Motivated by "non-abelian" analogues of standard conjectures on the cohomology of algebraic…
The aim of the paper is to discuss the relations between the three kinds of objects named in the title. In a sense, this is a survey of such relations; however, some new directions are also considered. This relates, especially, to sections…
the program of Langlands is studied here on the basis of: a)new concepts of global class field theory related to the explicit construction of global class fields and of reciprocity laws; b)the representations of the reductive algebraic…
A brief survey is given of the classical Langlands correspondence between n-dimensional representations of Galois groups of local and global fields of dimension 1 and irreducible representations of the groups GL(n). A generalization of the…
In this article we explore the interplay between two generalizations of the Whittaker model, namely the Klyachko models and the degenerate Whittaker models, and two functorial constructions, namely base change and automorphic induction, for…
In this short review, we pay attention to some subtleties in the study of projective representations, contrasting local to global properties and their interplay. The analysis is exposed rigorously, showing and demonstrating the main…
This paper introduces arithmetic geometry for polynomial identity algebras using non-commutative (formal) deformation theory. Since formal deformation theory is inherently local the arithmetic and geometric results that follow give local…
These notes provide a concise introduction to the representation theory of reductive algebraic groups in positive characteristic, with an emphasis on Lusztig's character formula and geometric representation theory. They are based on the…
We construct the ordinary irreducible representations of the group of automorphisms of a finite rooted tree and we get a natural parametrization of them. To achieve this goals, we introduce and study the combinatorics of tree compositions,…
Some notions of algebraic geometry can be defined for arbitrary varieties of algebras. This leads to universal algebraic geometry. The main idea of the presented theory is to consider interactions between algebra, logic and geometry in…
In this paper, we propose a framework to extract the algebra of the transformations of worlds from the perspective of an agent. As a starting point, we use our framework to reproduce the symmetry-based representations from the…