Electronic Journal of Differential Equations, Conference 04 (2000), pp. 17-22. Title: Quantization and irreducible representations of infinite-dimensional transformation groups and Lie algebras Author: Paul R. Chernoff (Univ. of California, Berkeley, CA, USA) Abstract: We present an analytic version of a theorem of Burnside and apply it to the study of irreducible representations of doubly-transitive groups and Lie algebras. Application to the Dirac quantization problem is given. Published July 12, 2000. Math Subject Classifications: 22E65, 17B15. Key Words: Infinite dimensional Lie algebras; representations.