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

@inproceedings{Langlands1990RepresentationT, title={Representation Theory ∗ Its Rise and Its Role in Number Theory}, author={R. 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 one hand. So called automorphic functions to… Expand

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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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