Extended affine su(2)(k) and restricted U(q) sl(2)

Global gauge symmetry becomes more intricate in low dimensional QFT. We survey the mathematical concepts leading to the relevant analogues of the (D=4) Doplicher-Haag-Roberts theory of superselection sectors and internal symmetry. We also review a recently uncovered duality between braid and quantum group representations in an extension of the chiral su(2)_k WZNW model for nonnegative integer level k.

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11 pages, extended version of a talk at the International Workshop 'Lie Theory and Its Applications in Physics VII' (Varna, Bulgaria, June 2007), to appear in the proceedings (eds. V. Dobrev et.al., Heron Press, Sofia)

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