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We provide explicit presentations of members of a suite of R matrices arisingfrom the (\dot{0}_m|\alpha) representations of the quantum superalgebrasU_q[gl(m|1)]. Our algorithm constructs both trigonometric and quantum Rmatrices; all of which are graded, in that they solve a graded Yang-Baxterequation. This grading is easily removed, yielding R matrices that solve theusual Yang-Baxter equation. For m>2, the computations are impracticable for ahuman to perform, so we have implemented the entire process in Mathematica, andthen performed the computations for m=1,2,3 and 4.

FOUR EASY PIECES — EXPLICIT R MATRICES FROM THE $(\dot 0_m |\alpha)$ HIGHEST WEIGHT REPRESENTATIONS OF Uq[gl(m|1)]

FOUR EASY PIECES — EXPLICIT R MATRICES FROM THE $(\dot 0_m |\alpha)$ HIGHEST WEIGHT REPRESENTATIONS OF U_q[gl(m|1)]