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

Abstract

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.

arXiv comment16 pages, latex, no figures

References in corpus (2)

• Identical Particles and Quantum Symmetries
• More on quantum groups from the the quantization point of view

Cited by in corpus (4)

• Identical Particles and Quantum Symmetries
• Integrable Hopf twists, marginal deformations and generalised geometry
• The Drinfeld-Kohno theorem for the superalgebra $gl(1|1)$
• Drinfeld twist for quantum $su(2)$ in the adjoint representation