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Four Easy Pieces--Explicit R. Matrices from the (Om | alpha) Highest Weight Representations of Uq[gl(m | 1)]

D. De Wit
Journal / Anthology

Year: 2000

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.

*Mathematics > Topology
*Science > Physics > Quantum Physics