• Hermann Weyl and Representation Theory

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    • Keywords


      Keywords Lie groups, gauge theory, epigenvalues, unitarian trick, character formula, Peter–Weyl theorem.

    • Abstract


      Weyl was a universal mathematician whose fundamental contributionsto mathematics encompassed all areas, and provideda unification seldom seen. His work on the theory ofLie groups was motivated by his life-long interest in quantummechanics and relativity. When Weyl entered Lie theory,it mostly focussed on the infinitesimal, and he strove to bringin a global perspective. Time and again, Weyl’s ideas arisingin one context have been adapted and applied to wholly newcontexts. In 1925–26, Weyl wrote four epochal papers in representationtheory of Lie groups which solved fundamentalproblems, and also gave birth to the subject of harmonic analysisof semisimple Lie groups. In these papers, Weyl provedcomplete reducibility theorems and introduced many techniqueswhich have become the standard way to study representationsof Lie groups and their various generalizationsin the last seven decades. Weyl’s work covers several parts ofmathematics, as well as parts of physics. In this article, wediscuss mainly his contributions to the representation theoryof Lie groups via the four papers mentioned above.

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