Four Easy Pieces - Explicit R Matrices from the (\dot{0}_m|\alpha) Highest Weight Representations of U_q[gl(m|1)]

Abstract

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