Special Functions and Representations of su(2)

Abstract

Here we present a general approach to integrating representations of a Lie algebra that are explicitly presented acting on quotients of the universal enveloping algebra (or as equivalent induced representations). The idea is to think of “group elements” as “non-commutative generating functions” for the representations. One can then shift from non-commutative elements acting on non-commutative elements to non-commutative operators acting on (functions of) commutative variables. The representation so transformed is thus typically presented in terms of differential operators and the usual boson operator calculus can be applied for performing computations.