# Representation Theory ∗ Its Rise and Its Role in Number Theory

@inproceedings{Langlands1990RepresentationT, title={Representation Theory ∗ Its Rise and Its Role in Number Theory}, author={Robert P. Langlands}, year={1990} }

By representation theory we understand the representation of a group by linear transformations of a vector space. Initially, the group is finite, as in the researches of Dedekind and Frobenius, two of the founders of the subject, or a compact Lie group, as in the theory of invariants and the researches of Hurwitz and Schur, and the vector space finite-dimensional, so that the group is being represented as a group of matrices. Under the combined influences of relativity theory and quantum…

## 15 Citations

Motives and Infinite Primes

- Mathematics
- 2011

In algebraic geometry the notion of variety defined by algebraic equation is very general: all number fields are allowed. One of the challenges is to define the counterparts of homology and…

Langlands Program and TGD

- Mathematics
- 2007

Number theoretic Langlands program can be seen as an attempt to unify number theory on one hand and theory of representations of reductive Lie groups on the other hand. So called automorphic…

Langlands Program and TGD

- Mathematics
- 2007

Number theoretic Langlands program can be seen as an attempt to unify number theory on one hand and theory of representations of reductive Lie groups on one hand. So called automorphic functions to…

Hessian polyhedra, invariant theory and Appell hypergeometric partial differential equations

- Mathematics
- 2004

It is well-known that Klein's lectures on the icosahedron and the solution of equations of fifth degree is one of the most important and influential books of 19th-century mathematics. In the present…

Introduction to the Langlands Program

- Mathematics
- 2000

This article is an introduction to automorphic forms on the adeles of a linear reductive group over a number field. The first half is a summary of aspects of local and global class field theory, with…

Geometric Endoscopy and Mirror Symmetry

- Mathematics
- 2007

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…

TGD as a Generalized Number Theory

- Mathematics
- 2009

The focus of this book is the number theoretical vision about physics. This vision involves three loosely related parts.
The fusion of real physic and various p-adic physics to a single coherent…

Langlands correspondence and Bezrukavnikov's equivalence

- Mathematics
- 2019

This document contains notes from a course taught by Geordie Williamson at the University of Sydney in 2019-2020. The primary goal of these lectures was to give an informal introduction to what the…

Splitting primes

- Mathematics
- 2010

Groups, rings, fields, polynomials, primes, functions : most mathematics students at the university have come across these concepts. It so happens that one of the basic problems of number theory can…

Characters and Representations After 1897

- Mathematics
- 2013

Frobenius’ papers of 1896–1897 marked the beginning of a new theory, a theory that continued to evolve in various directions for over a half-century. Frobenius himself, along with Burnside, made…

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