Yassen S. Stanev, Ivan T. Todorov
On Schwarz Problem for the $\widehat{su}_2$ Knizhnik-Zamolodchikov Equation
The paper is published: Lett. Math. Phys. 35 (1995) 123-134

MSC:

17B37 Quantum groups and related deformations, See also {16W30, 81R50, 82B23}

81R10 Representations of infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody and other current algebras, See also {17B65, 17B67, 22E65, 22E67, 22E70}

81R50 Quantum groups and related algebraic methods, See Also {16W30, 17B37}

81T40 Two-dimensional field theories, conformal field theories, etc.

Abstract: We study the monodromy representations $\Cal B^{k,I}$ of the mapping
class group $\Cal B_4$ acting on 4-point blocks satisfying the
Knizhnik-Zamolodchikov equation for the level $k$ $su_2$ current
algebra. We classify all irreducible $\Cal B^{k,I}$ which are
realized by finite groups; we also display finite irreducible
components for the reducible representations corresponding to $k=10$.

Keywords: monodromy representations, mapping class group, Knizhnik-Zamolodchikov equation, current algebra