Multiparameter Quantum Groups and Multiparameter R-Matrices

摘要

There exists an (sub 2, sup n) + 1 parameter quantum group deformation of GL(subn) which has been constructed independently by several (groups of) authors. In this note the author gives an explicit R-matrix for this multiparameter family. This gives additional information on the nature of this family and facilitates some calculations. This explicit R-matrix satisfies the Yang-Baxter equation. The center of the paper is section 3 which describes all solutions of the YBE under the restriction r(sub cd, sup ab) = 0 unless (left brace) a, b (right brace) = (left brace) c, d (right brace). One kind of the most general constituents of these solutions precisely corresponds to the (sub 2, sup n) + 1 parameter quantum group mentioned above. The author describes which solutions extend to an enhanced Yang-Baxter operator and hence define link invariants. The paper concludes with some preliminary results on these link invariants.