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

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

2000-05-05

arxiv.org/abs/math/0005049v1

International Journal of Modern Physics C: Physics and Computers 12(7):(September 2001) 1109-1136

Mathematics

Quantum Algebra

17 pages (10 are in an appendix), 1 table. David De Wit: <http://www.kurims.kyoto-u.ac.jp/~ddw/>

Scientific paper

10.1142/S012918310100236X

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.

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