Quantum Groups and Homology of Local Systems

Abstract

From the text: ``In this paper we `quantize' results of Part IIof an earlier paper of ours [Invent. Math. 106 (1991), no. 1, 139194; MR 93b:17067]. We establish and study the connection between(co)homology of local systems introduced earlier [V. V.Schechtman and A. N. Varchenko, ``Integral representations of Npoint conformal correlators in the WZW model'', Preprint MPI/8951, Max Planck Inst. Mat., Bonn, 1989; Lett. Math. Phys. 20(1990), no. 4, 279 283; MR 92g:33027; op. cit.; MR 93b:17067] andhomology of nilpotent subalgebras of certain Hopf algebras veryclose to Drinfeld Jimbo q analogues of Kac Moody algebras. Themain result is an explicit version of the Kohno type theorem`half monodromy = R matrix'. Details of proofs will bepublished elsewhere.''\par {For the entire collection see MR94h:14002.}