
Introduction 11
discussed the symbolical content of Hargreaves’s results and introduced for that purpose
symbols π and ρ satisfying
πρ −ρπ = α, (1.14)
where α was assumed to commute with π and ρ. Graves discussed that a particular represen-
tation for this commutation relation is given (for α =1)byπ → D =
d
dx
and ρ → X,where
X denotes again the operator of multiplication with the independent variable x. He also
showed that this commutation relation implies an abstract version of Hargreaves’ results.
In fact, a few years earlier, in 1850, Donkin [362] had considered a more general situation
in which symbols ω, ρ
1
,...,ρ
n+1
are involved which satisfy
ωρ