Four Easy Pieces - Explicit R Matrices from the (\dot{0}_m|\alpha) Highest Weight Representations of U_q[gl(m|1)]
Quantum Algebra
2009-10-31 v1
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.
Keywords
Cite
@article{arxiv.math/0005049,
title = {Four Easy Pieces - Explicit R Matrices from the (\dot{0}_m|\alpha) Highest Weight Representations of U_q[gl(m|1)]},
author = {David De Wit},
journal= {arXiv preprint arXiv:math/0005049},
year = {2009}
}
Comments
17 pages (10 are in an appendix), 1 table. David De Wit: <http://www.kurims.kyoto-u.ac.jp/~ddw/>