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

Abstract

We provide explicit presentations of members of a suite of R matrices arising from the [Formula: see text] representations of the quantum superalgebras Uq[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.