On the Drinfel'd-Kohno Equivalence of Groups and Quantum Groups

Details On the Drinfel'd-Kohno Equivalence of Groups and Quantum Groups On the Drinfel'd-Kohno Equivalence of Groups and Quantum Groups

1995-09-05

arxiv.org/abs/q-alg/9509001v1

Mathematics

Quantum Algebra

16 pages, latex, no figures

Scientific paper

A method to calculate matrix representations of the twist element $\ff$ of Drinfel'd -- chosen to be unitary -- is given and illustrated at some examples. It is observed that for these F-matrices the crystal limit $q\!\to\! 0$ exists and that \mbox{F-matrices} twisting from $0$ to $q$ are of a simpler form than F-matrices twisting from $1$ to $q$. These results lead to a new interpretation of $q$-deformation in terms of tensor products of finite-dimensional representations of compact simple Lie groups.

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