MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).

2 typo fixed

At the first glance it appears that he more or less just gave the first nontrivial example(s) of waht what was latter later called the Casimir operators.

His obituary says:

On 1 May 1931 he wrote a letter from The Hague to the famous G¨olttingen Gottingen mathematician Hermann Weyl and announced: ‘While studying the quantum-mechanical properties of the asymmetic rotator I arrived at some ‘results’ (?) concerning the representation of continuous groups.’ He then sketched his findings on the matrix elements of the irreducible representations for the three-dimensional rotation group, and a possible extension for semi-simple groups in general, where he introduced what was later called the ‘Casimir operator’. This operator turned out to be a multiple of the unit-operator and may be used to characterize in an elegant way the irreducible representations of a given continuous group. To Casimir’s question, ‘Whether the case is worth considering?’, Weyl answered definitely ‘Yes’. Hence the Leiden doctoral candidate published his mathematical results in a paper, communicated by Ehrenfest to the meeting of 27 June 1931 of the Amsterdam Academy [7], and he also included them as Chapter IV of his dissertation, which he defended on 2 November 1931 at the University of Leiden [8].

1

At the first glance it appears that he more or less just gave the first nontrivial example(s) of waht was latter called the Casimir operators.

His obituary says:

On 1 May 1931 he wrote a letter from The Hague to the famous G¨olttingen mathematician Hermann Weyl and announced: ‘While studying the quantum-mechanical properties of the asymmetic rotator I arrived at some ‘results’ (?) concerning the representation of continuous groups.’ He then sketched his findings on the matrix elements of the irreducible representations for the three-dimensional rotation group, and a possible extension for semi-simple groups in general, where he introduced what was later called the ‘Casimir operator’. This operator turned out to be a multiple of the unit-operator and may be used to characterize in an elegant way the irreducible representations of a given continuous group. To Casimir’s question, ‘Whether the case is worth considering?’, Weyl answered definitely ‘Yes’. Hence the Leiden doctoral candidate published his mathematical results in a paper, communicated by Ehrenfest to the meeting of 27 June 1931 of the Amsterdam Academy [7], and he also included them as Chapter IV of his dissertation, which he defended on 2 November 1931 at the University of Leiden [8].