Monodromy representations of braid groups and Yang-Baxter equations. (English) Zbl 0634.58040

Kohno, Toshitake

Ann. Inst. Fourier 37, No. 4, 139-160 (1987).

Motivated by the two-dimensional conformal field theory with gauge symmetry, we study the monodromy of the integrable connections associated with the simple Lie algebras. This gives a series of linear representations of the braid group whose explicit form is described by solutions of the quantum Yang-Baxter equation.

Reviewer: T.Kohno

MSC:

17B65	Infinite-dimensional Lie (super)algebras
58A15	Exterior differential systems (Cartan theory)
58F07	Completely integrable systems (including systems with an infinite number of degrees of freedom) (MSC1991)

Keywords:

two-dimensional conformal field theory; gauge symmetry; integrable connections; simple Lie algebras

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