Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (0̇m|α̇n) representations of Uq[gl(m|n)] Original Researc

We detail the automatic construction of R matrices corresponding to (the tensor products of) the (0̇m|α̇n) families of highest-weight representations of the quantum superalgebras Uq[gl(m|n)]. These representations are irreducible, contain a free complex parameter α, and are 2mn-dimensional. Our R matrices are actually (sparse) rank 4 tensors, containing a total of 24mn components, each of which is in general an algebraic expression in the two complex variables q and α.Although the constructions are straightforward, we describe them in full here, to fill a perceived gap in the literature. As the algorithms are generally impracticable for manual calculation, we have implemented the entire process in Mathematica; illustrating our results with Uq[gl(3|1)].