Just a historical comment (from my memory; I am at the moment rather far from the subject)

Ivan Todorov gave and wrote few times lectures about the history of Sugawara construction to which he himself also contributed. He even mentions some works in late 1940-s in field theory of photons among curioous early occurences and then the intricate history in 1960's and 1970's, involving Kac, Gel'fand-Fuks, Sugawara, Segal, Todorov etc. Sugawara is in any case not the first in that sequence and he had a wrong proportionality constant calculated, what is corrected in 1970s.

It is also curious that the (affine) Sugawara construction is not confined to working over complex numbers, there is a more general version overmore general fields explained by Faltings. I think I have seen it in his paper (I do not have it here so I can not check)

Gerd Faltings, A proof for the Verlinde formula.  J. Algebraic Geom.  3  (1994),  no. 2, 347--374. MR1257326 (95j:14013)