# 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… Expand

#### 15 Citations

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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… Expand

Langlands Program and TGD

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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… Expand

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Introduction to the Langlands Program

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- 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… Expand

Geometric Endoscopy and Mirror Symmetry

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- 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… Expand

TGD as a Generalized Number Theory

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The focus of this book is the number theoretical vision about physics. This vision involves three loosely related parts.
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Langlands correspondence and Bezrukavnikov's equivalence

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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… Expand

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