The early development of the representation theory of semisimple Lie groups: A. Hurwitz, I. Schur, H. Weyl
type: Item
instance of: scholarly article
title: The early development of the representation theory of semisimple Lie groups: A. Hurwitz, I. Schur, H. Weyl
zbMATH Open document ID: 0983.01010
published in: Jahresbericht der Deutschen Mathematiker-Vereinigung (DMV)
publication date: 2002-04-19T00:00:00Z
review text: This article starts from the celebrated ``character formula'' by H. Weyl, and then looks back to the work by \textit{A. Hurwitz}, The invariant integral on Lie groups in 1897. Meanwhile, \textit{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 \textit{F. Peter} in 1927 [Math. Ann. 97, 737-755 (1927; JFM 53.0387.02)].
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 22-03
Mathematics Subject Classification ID: 22E45
zbMATH DE Number: 1346291
zbMATH Keywords: JFM 53.0387.02
author: Peter Slodowy
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1346291