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The early development of the representation theory of semisimple Lie groups: A. Hurwitz, I. Schur, H. Weyl. (English) Zbl 0983.01010
This article starts from the celebrated “character formula” by H. Weyl, and then looks back to the work by A. Hurwitz, The invariant integral on Lie groups in 1897. Meanwhile, I. Schur determined the irreducible polynomial representations of \(\text{GL}_n\), developed a character formula in his dissertation (1901). Weyl, in a letter to I. Schur in 1924, sketched the four sections: 1) Introduction; 2) The derivation of the integral formula for the unitary groups; 3) The derivation of the character and dimension formula for unitary groups; 4) A sketch of 2), 3) for semisimple groups. The definite breakthrough had to wait until his joint work with F. Peter in 1927 [Math. Ann. 97, 737-755 (1927; JFM 53.0387.02)].

01A60 History of mathematics in the 20th century
22-03 History of topological groups
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
JFM 53.0387.02