Four easy pieces - Explicit R matrices from the (O-m broken vertical bar alpha) highest weight representations of U-q[gl(m broken vertical bar 1)]

We provide explicit presentations of members of a suite of R matrices arisi ng from the ((0) over dot (m)/alpha) representations of the quantum superal gebras U-q[gl(m\1)]. Our algorithm constructs both trigonometric and quantu m R matrices; all of which axe graded, in that they solve a graded Yang-Bax ter equation. This grading is easily removed, yielding R matrices that solv e the usual Yang-Baxter equation. For m > 2, the computations are impractic able for a human to perform, so we have implemented the entire process in M ATHEMATICA, and then performed the computations for m = 1, 2, 3 and 4.