Infinite commutative product formulas for relative extremal projectors

Loosely speaking, a relative extremal projector is a universal projector mapping any appropriate representation onto a certain highest subrepresentation. This paper presents a number of infinite product expansions for the relative extremal projector, most of which are new even for the extremal projector. As an application, conditions are given determining when the relative extremal projector descends to a well-defined operator on a particular representation. The total denominator and related summation formulas are also studied.