Hermann Weyl

Hermann Weyl (November 9 1885 - December 8 1955) was a German mathematician. Although much of his working life was spent in Zürich and then Princeton, he is closely identified with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski. His research has had major significance for theoretical physics as well as pure disciplines including number theory. He was one of the most influential mathematicians of the twentieth century, and a key member of the Institute for Advanced Study in its early years, in terms of creating an integrated and international view.

Topological groups, Lie groups and representation theory

See main articles Peter-Weyl theorem, Weyl group, Weyl spinor,Weyl algebra

Related Topics:
Peter-Weyl theorem - Weyl group - Weyl spinor - Weyl algebra

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From 1923 to 1938, Weyl developed the theory of compact groups, in terms of matrix representations. In the compact Lie group case he proved a fundamental character formula.

Related Topics:
1923 - 1938 - Compact group - Matrix representation - Compact Lie group - Character formula

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These results are foundational in understanding the symmetry structure of quantum mechanics, which he put on a group-theoretic basis. This included spinors. Together with the mathematical formulation of quantum mechanics, in large measure due to John von Neumann, this gave the treatment familiar since about 1930. Non-compact groups and their representations, particularly the Heisenberg group, were also deeply involved. From this time, and certainly much helped by Weyl's expositions, Lie groups and Lie algebras became a mainstream part both of pure mathematics and theoretical physics.

Related Topics:
Quantum mechanics - Spinor - Mathematical formulation of quantum mechanics - John von Neumann - Heisenberg group - Lie algebra - Pure mathematics - Theoretical physics

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His book The Classical Groups, a seminal if difficult text, reconsidered invariant theory. It covered symmetric groups, full linear groups, orthogonal groups, and symplectic groups and results on their invariants and representations.

Related Topics:
Invariant theory - Symmetric group - Linear group - Orthogonal group - Symplectic group - Invariant - Representation

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